D.C. School Superintendent Vincent E. Reed, saying he was weary from "five years of bull. . . .," submitted his formal resignation yesterday -- touching off an appeal from Mayor Marion Barry for reconsideration, a widespread sense of community loss and tears in the eyes of some school administrators.

In a one-sentence letter of resignation sent to school board president R. Calvin Lockridge, Reed wrote:

"After much agonizing thought, I have decided to retire from the District of Columbia public schools effective Dec. 31. Respectfully, Vincent E. Reed, Superintendent of Schools."

Later, Reed told reporters, "I'm just tired of the five years of bull. . . . You can set down a glass and drip water in it drop by drop, and sooner or later it fills up. How much can you take?"

Replying to Reed's letter, Lockridge wrote that he was "very sorry" the superintendent had resigned and asked to meet with him soon "so that . . . I can benefit from your wisdom and experience to make sure an orderly transition will occur."

Even though Reed named Lockridge as one of the board members who had frequently obstructed him, the board president praised Reed in an interview as a man "I personally like and respect very much." He said he met with Reed on Monday and urged him not to resign.

Another board member, Carol Schwartz, who reed said generally supported him, said she would meet with the superintendent today to urge him to reconsider. "It's difficult for board members to say they don't want Reed because Vince Reed is so popular," she remarked. "But for some members there's a big embracing [of the superintendent] and the behind-the-scenes undercutting that constantly goes on."

Reed told reporters: "The reason I'm leaving is not so much because of any one set of issues.It's not the kind of thing you can put your hand on. It is attitude and relationships, how they talk to you. They [the members of the board] were nasty to me. I guess I was nasty back, too.

Reed left open the possibility that he might change his mind: "At this moment," he said, "[resignation] is my decision. I have two weeks, and I don't want to say anything is forever. I don't want to leave, but I don't want people to think I'm playing a game. It's a vague answer, but I'm doing it intentionally."

The Reed who greeted reporters yesterday in his roomy office filled with the trophies and memorabilia of 27 years in the public school system was a relaxed and almost jovial contrast to the one who sat stone-faced, quietly taking notes at Wednesday night's school board meeting.

There was no sign of the man described by one friend yesterday as having undergone a "kind of Chinese water torture at the hands of the city's school board over the last few months.

Reed's executive assistant and longtime associate William Saunders said Reed had lost considerable weight at the insistence of his doctor because of high blood pressure brought on by the pitched personal battles between Reed and the politically charged school board.

"He and his wife really seriously discussed the fact that he didn't want to get to the point where he got a heart attack," said George Margolies, the school administration's lawyer.

Barry knew earlier this week that Reed was contemplating quitting, sources said, and on Tuesday encouraged Reed to stay on the job. In a prepared statement issued yesterday, the mayor said that while he was "reluctant to involve myself in any official way in the problems that exist between the superintendent and the Board of Education, I want to make it clear to them and to the public that, for the sake of our children and the preservation of public education in this city, we need superintendent Reed to stay on."

Noting that he and Reed have had "a few differences in the past, an apparent reference to their jostling in recent months over the size of the school system's budget, Barry praised Reed's "strong, dedicated and effective leadership." He said the loss of Reed "would seriously disrupt efforts to improve the school system."

According to Barry's press spokesman, Alan Grip, the mayor phoned Reed at 12:30 p.m. yesterday to again ask him to reconsider. Grip said Reed "did not say he would not reconsider."

Reed, 52, will be eligible to receive 50 percent of his $54,000 annual salary by retiring before Jan. 1, when new retirement provisions become effective, he said. Under the new regulations, Reed would have to be 55 to obtain comparable benefits.

Reed said the early retirement option was only the factor in his decision and not a significant one. His three-year contract expires on March 1982.

The school superintendent, who has long been considered one of the most popular city officials in the District, also told reporters yesterday that he even thought Lockridge said he has heard rumors that Reed had been urged to do so by some prominent whites.

"If I really was a politician, I wouldn't be in the shape I am now," Reed said.

The superintendent said he had been offered a $125,000-a-year job earlier this year as head of the Chicago public schools earlier this year but has "absolutely" no interest in taking that job.

Reed also said local Republicans had asked if he was interested in serving in the Reagan administration, but has received no firm offers. He said he would "have to wait to see what it is" before deciding to take any federal post.

Late yesterday afternoon, standing in front of a Christmas tree on an auditorium stage at Taft Junior High School, Reed became tearful when a group of about 400 school adminstrators gave him a standing ovation. Wiping his eyes with a white handkerchief, he gestured for them to stop. He spoke for 10 minutes. Some of his staff members called it a farewell address.

I've reached the point with the board that I feel the relationship is counterproductive to [operating the school system]," Reed said. "There are some board members who are trying to hamper the superintendent from running the school system on a day-to-day basis. . . . Some of the things that go on downtown are unbelievable."

"The agony of what I've been through is something I can't explain. It's something I can't stand anymore," Reed said.

When he finished, the audience stood, clapping. But Reed left the stage quickly, walking up a side aisle as if he wanted to quell the outburst of support. He was besieged by well-wishers, women who hugged and kissed him, some bursting into tears. Many of the men patted him on the back. Reed smiled an easy smile. "I'm okay," he reassured, "You'll be all right in a while."

When he announced his pending resignation Wednesday, Reed said his departure had been prompted by what he considered improper efforts by the board to take over day-to-day school operations, its attitude toward his staff and its rejection of his proposal for an academic high school.

Besides Lockridge, he said the board members who had been meddlesome and obstructive were John Warren ("He's number one," Reed remarked), Bette Benjamin, and Eugene Kinlow.

When asked last night about Reed's criticism, Lockridge said, "I have always tried to cooperate with the superintendent . . . Yes, the board has become more concerned with the implementation of policy, and that can be construed as interference. I wouldn't construe it that way.

"I think that Dr. Reed, like myself, has become frustrated at the pain of the budget cuts," Lockridge continued. "He's frustrated. I'm frustrated. It's hard to be in this."

Before Reed took office in 1975, the school system had been headed by four superintendents and two acting superintendents in eight years. During his five-year tenure Reed became known as a non-nonsense administrator, one who emphasized a back-to-basics approach instead of experimental educational programs. He was also a product of the school administration, unlike the three superintendents who preceded him and were considered "outsiders" by the school administrators.

Reed was appointed school superintendent in October 1975. Many considered him a breath of fresh air when compared with his predecessor, Barbara A. Sizemore, whose administration was riddled with controversy, stormy school board meetings and occasional racial polorization.

Reed's administration was pummeled by a 23-day teacher strike in March 1979 and the loss of 700 teachers last summer through Barry's financial austerity program. But during his tenure, District public school students improved their test scores on national achievement tests two years running, after a decade of deterioration. And many who previously had no confidence in the schools saw new hope.

Hundreds of callers telephoned Reed's office and local radio stations yesterday, including a widespread sense of loss at the departure of Reed and fear of what might happen to the school system when he leaves. Virtually all the callers pledged support for Reed and urged him to reconsider.

Lockridge said the board would meet before Dec. 31 to pick an acting superintendent to succeed Reed. He said several top administrators, including vice superintendent Elizabeth Yancey, would be considered for the slot.