A massive wave of more than 250,000 persons gathered around the Washington Monument and marched to the Capitol yesterday to protest President Reagan's budget cuts and tax policies and to reaffirm the solidarity of the nation's labor movement behind its leaders.

Yesterday's Solidarity Day demonstration, organized by the AFL-CIO and civil rights groups and partly inspired by the successful workers' movement in Poland, was unprecedented in modern labor history and perhaps the largest political protest in Washington during the past 20 years. City officials reported only two arrests, both for minor incidents of disorderly conduct. In another incident,a CBS reporter was injured when he was ejected from a restricted area.

The crowd was a broad slice of America -- a 38-year-old tool maker from Cincinnati who complained that only the rich were getting a break; a fourth-grade school teacher from Mahopac, N.Y., wearing a long flowing black cape bedecked with protest buttons, angry over cutbacks in the school lunch program.

There were ironworkers from New Jersey, sipping beer while they lamented the shortage of jobs; farm workers marching under protest placards printed in Spanish; unionized artists chanting "No Business Like Show Business" as they joined the procession.

Municipal employes from Midwestern cities were there, clamoring for adoption of the Equal Rights Amendment. Senior citizens came up from a Charlottesville, Va., nursing home to voice their fears of cutbacks in Social Security. Blacks, whites, Hispanics and others joined hands as they sang "We Shall Overcome" at the end of the day's events.

It was a colorful patchwork of men, women and children wearing dozens of hues of matching paper hats and hoisting forests of multicolored protest signs. The parade strung out for more than a mile down Constitution Avenue in the heart of the nation's capital.

"If you do not embrace the proposition that this president has a mandate to destroy the programs that feed the roots of a decent society, look about you," AFL-CIO president Lane Kirkland told the sprawling crowd of protesters gathered under overcast afternoon skies. "You are not alone."

The message of the rally should be clear, even to a president who spent the day 65 miles away at Camp David, Kirkland said: Reagan can no longer claim to speak for the average American worker.

Kirkland delivered a stinging indictment of the Republican administration. He said Reagan's tax-cut program, which mostly benefits the rich, was proving to be the "most irresponsible fiscal act of our time." He also accused the administration of pursuing monetary policies that caused record-high interest rates.

"They are sacrificing the homes, health and hopes of millions on the altar of crank economic abstractions that defy the laws of simple arithmetic and dismay even their friends on Wall Street," Kirkland said.

The labor movement's warnings were echoed by representatives of various civil rights' and women's groups who shared the spotlight.

"We will not sit idly by while the bare necessities of life are taken from the needy and given to the greedy," said Benjamin L. Hooks, executive director of the NAACP. "We're saying to those who have $1,000 boots, while our children have no shoes, 'Well, no, we won't take that,' " he said.

Though President Reagan was not present, he received reports of the rally by telephone. White House spokesman David Gergen said that even though the demonstration was aimed at Reagan, the president believed "that the true enemy of working men and women is a sick economy.

"The president recognizes and appreciates the frustration that comes because there are no instant miracles and he also appreciates the fact that the medicine is hardly sweet," Gergen said.

U.S. Park Police officially estimated the crowd at just under 260,000, more than twice the number predicted by the AFL-CIO and about 60,000 more than forecast by the National Park Service. The Park Service based its count on aerial surveillance from a helicopter and by counting the buses parked on the Mall and at satellite parking lots near Metro stops.

Yesterday's crowd was apparently slightly larger than the 250,000 who took part in an anti-Vietnam War Moratorium rally on the grounds of the Washington Monument on Nov. 15, 1969, and more than the officially estimated 200,000 who participated in the March on Washington led by the late Rev. Martin Luther King Jr. on Aug. 28, 1963.

It was also larger than the 175,000 who gathered for the mass on the Mall celebrated by Pope John Paul II on Oct. 7, 1979 and the 200,000 who took part in the Washington for Jesus rally April 29, 1980. It did not, however, rival the crowds of 500,000 and more that have witnessed presidential inaugurals and the U.S. hostage motorcade on Jan. 28, 1981.

U.S. Park Police Maj. Larry Finks said his men counted 4,418 buses with an average of 45 persons each, for a total of 198,810 people. An additional 8,750 demonstrators came by train or other buses, he said, and an additional 52,000 came by car or on foot.

By early afternoon, more than 160,000 persons had riden the Metro subway into downtown Washington and a similar number were expected to ride out, equaling the number of people that usually use the train on a weekday. The subway ran free all day because Solidarity Day organizers leased it at a cost of $65,000.

Early in the day, crowds arriving at RFK Stadium found the system so full that 25-minute waits for a train were common. Many walked the nearly 30 blocks to the staging area at the Washington Monument.

As the crowd began to leave around 4:30, an outbound train at the Stadium-Armory station developed brake problems, forcing Metro to use only one lane, alternating for inbound and outbound trains. Full service was restored about an hour later.

The injured reporter, CBS news reporter Lemuel Tucker, was in the restricted area set aside for entertainers and featured speakers when a rally marshal ejected him, according to a U.S. Park Police spokesman. No charges were placed and the marshal was not identified, the spokesman said. Tucker was listed in good condition last night at George Washington University Hospital, with three fractured ribs, a bruised lung and a possible damaged spleen.

Most of the demonstrators shunned commercial air travel in sympathy with the striking air traffic controllers. Some went to great lengths to keep the faith.

For instance, AFL-CIO members from Seattle, Wash., canceled a direct flight here and instead drove to Vancouver, British Columbia, hopped aboard a Canadian airlines flight across Canada to Toronto and then made a 13 1/2 hour bus ride to Washington.

"There was no way we were going to cross the picket line," yawned Roger Yockey, an official of the Retail Store Employees Union who made the trip. "I'm wiped out -- my rear end especially -- and the air conditioning broke on the bus. But it was well worth it for this historical event."

Though more than 200 civil rights, environmental, womens' rights and other groups worked with the AFL-CIO in planning the event, the seven-hour march and rally had an unmistakable union flavor to it.

The crowd began filling up the Ellipse and Monument grounds before 10 a.m. As bluegrass, folk and soul music lent a festive air to the gathering, burly machinists and mine workers in T-shirts, nylon windbreakers and baseball caps stood side-by-side with antinuclear activists, gay rights advocates and thousands of municipal workers.

Vendors were kept busy as long lines formed for hot dogs, buttons, banners and badges. At one stand, a "Kennedy in '84" button was moving slowly, but outselling one that announced, "I support PATCO."

Marching bands and thousands of bright yellow, white and red balloons added to the festive air, as the demonstrators began lining up for the march.

Some of the protestors stood in line for the regularly scheduled morning tour of the White House, before assembling by the Washington Monument.

The march, which was to take more than three hours to complete, began sharply at noon. Leading the way were Kirkland; Thomas Donahue, secretary-treasurer of the AFL-CIO; Coretta Scott King, widow of the slain civil rights leader and co-chairman of the Full Employment Action Council; Bayard Rustin, chairman of the A. Philip Randolph Institute; Vernon E. Jordan, outgoing president of the National Urban League; Tony Bonilla, president of the League of United Latin American Citizens; Eleanor Smeal, president of the National Organization of Women (NOW), and Hooks of the NAACP.

The vast procession moved briskly from 14th Street east along Constitution Avenue towards the Capitol, to the smart, stirring beat of the high-stepping bands from Cardozo and McKinley high schools here.

Some demonstrators who apparently had never seen the national labor and civil rights leaders stood along the parade route, craning their necks. "Who's that tall black man? It isn't Vernon Jordan, is it?" hollered Bill Steyert, an environmentalist who drove from Chicago for the rally. It was Jordan.

Some of the demonstrators chanted, "Hey, hey, he's no good. Send him back to Hollywood," a reference to Reagan's former days as an actor. A group from the American Federation of State, County and Municipal Employees chanted "Hey, Hey, Ho, Ho, Reagan's Got to Go" as they passed the headquarters of the U.S. Department of Labor.

A group of senior citizens from Charlottesville carried signs saying, "We paid for Social Security, not for a safety net" and "Social Security is help when help is needed." One Detroit auto worker bore a placard that read, "Dim Jim Watt," the Reagan administration's secretary of the interior.

The procession turned south at Third Street and filed onto the Mall on the apron of the Capitol.

The speeches at the Capitol were the high point of the day, and many who came had grown restless waiting for them. "It's very frustrating to see the apathy here," said Mark Zola, 37, a steelworker from McKeesport, Pa., before the talking began.

"We should have been here during the week to shut down Washington," said Ron Weisern, president of Steelworkers Local 1397 of Homestead, Pa. "This day is just a sham. We're accomplishing nothing, showing up on the weekend. We came to show union support, but it's not going to change a thing, really."

The scene on the Mall suggested a festive crowd more than disgruntled Americans, but the words of the speakers clearly voiced a strong fear of the future under a Reagan administration and hope for more influence on the part of the labor movement and the old Democratic coalition.

"We did not choose this battle, it was thrust upon us by President Reagan, a president who claims to have a mandate from the people," said Sam Church Jr., president of the United Mine Workers of America. "Well, we are the people and I proclaim that if the battle must be, let it be."

Tony Bonilla, president of the League of United Latin American Citizens, said the protest was reminiscent of the early days of labor agitation led by John L. Lewis, founder of the mine workers union.

"We have marched today as John L. Lewis marched to preserve and enhance the dignity of America," Bonilla said.

The Rev. Jesse Jackson, president of Operation PUSH, said in an interview that the demonstration may be a sign that black and white workers were overcoming their racial differences in the face of common economic problems.

"Many of the white workers here today voted for Reagan," Jackson said. "But they are here now because they feel betrayed."

Sen. Patrick J. Leahy, (D-Vt.), a Reagan critic who attended the rally, also cautioned that Solidarity Day's impact may be long in coming in Congress. Its more immediate effect might be to create more awareness among rank-and-file union members of the consequences of Reagan's policies.

"I think it's true that labor has lost a lot of clout, but things like this rally will help to bring it back," he said. "Labor's power will come back. Things like this are cyclical."

Douglas A. Fraser, president of the United Auto Workers, accused the administration of resorting to "extreme and cruel" tactics when it fired 12,000 striking air traffic controllers. The plight of the striking air controllers was a rallying cry for some of the demonstrators, who accused Reagan of union busting.

Fraser said the Solidarity Day gathering "should serve notice on our enemies that the labor movement and its allies are ready to fight and struggle. And this turnout will hopefully stiffen the spine of some of our friends."

However, Jerry Wurf, president of the American Federation of State, County and Municipal Employees (AFSCME), the union with the largest contingent at the demonstration, cautioned against reading too much into the day's events.

"In spite of this turnout, there is no guarantee that our task will succeed," Wurf said. "This is a beginning of a long, difficult, frustrating process to turn the country around.