Washington's only memorial to an American labor leader, Samuel Gompers, slowly is falling apart, according to an engineering study by the National Park Service.

Gompers, who founded the American Federation of Labor in 1881 and was reelected as its president 42 times until his death in 1924, is immortalized in a 16-foot bronze statue in a small triangular park at 11th Street and Massachusetts Avenue NW.

Concern about the deterioration of the Gompers memorial has prompted the Metropolitan Washington AFL-CIO to renew its plan for a fund-raising drive to restore the site, and also to raise funds to erect a memorial to A. Philip Randolph, the nation's preeminent black labor leader.

Randolph founded the first major black union, the Brotherhood of Sleeping Car Porters, in 1925. The noted civil rights leader died in 1979.

"This is important because the lives of these men are the kind of thing the labor movement can not afford to lose track of," said Joslyn N. Williams, the labor council president. "If we lose track of where we've come from, we lose track of where we are going."

The Gompers memorial, built in 1933 and dedicated by President Roosevelt, features Gompers seated on a bronze pedestal surrounded by six bronze allegorical figures representing the labor movement. Roosevelt, at the dedication, hailed the efforts of Gompers, a Jewish immigrant cigar maker from England who welded the labor movement into a powerful force.

Roosevelt noted that he and Gompers had been branded "radicals" because they promoted such labor reforms as limiting women's working hours to 54 hours a week.

Congress had given permission to the AFL in 1928 to build the monument with its money on federal property.

An engineering study of the memorial showed "several serious problems" in the internal structural ironwork that holds together the bronze statues, according to Arnold M. Goldstein, assistant superintendent of the National Park Service's central region, which has responsibility for more than 50 statues erected with congressional approval.

Estimates for the repair work run to more than $50,000, according to Park Service spokeswoman Sandra Alley. She said that it is unclear how soon the Park Service could begin repairs but that private contributions wouldspeed the process.

The statue has developed numerous cracks, which appear to be deepening, and the erosion has affected the internal ironwork, according to the report prepared by Environmental Management Consultants for the Park Service. The statue would have to be dismantled and repairs made on the bronze, iron and granite base, the firm said.

The AFL-CIO donated $5,000 to launch a Gompers-Randolph fund drive in 1983, but a fund-raising effort by the local labor council was stalled by financial problems and by the death of its fund-raising chairman, Matt Romeo, the head of Sheet Metal Workers Local 100.

Williams said that D.C. Mayor Marion Barry had pledged to find a city-owned site for a Randolph monument, but Williams said the labor council has not decided what form of memorial to Randolph it wants to erect.

He said that the AFL-CIO would like to complete both projects by September 1986, when it hopes to revive the tradition of a Labor Day parade in Washington.