More than 100 black mayors convened in the nation's capital yesterday, and though their first order of business - an appeal for federal funds - was not unpredictable, the cause they were backing was - the plight of the small town.

The mayors were attending the third annual meeting of the National Conference of Black Mayors, an organization born out of the dramatic increase in black elected officials that has followed the black political gains of the civil rights movement.

The mention of black mayors usually brings to mind those blacks who have been chosen to head large urban centers, like Coleman Young of Detroit, Thomas Bradley of Los Angeles, Maynard Jackson of Atlanta and Kenneth Gibson of Newark.

But most of the 161 black mayors are from small, often rural areas in the South - like Cotton Plant, Ark., Waterproof, La. and Mound Bayou, Miss. - and non-Southern, heavily black suburban areas - such as Centreville, Ill. and Urbancrest, Ohio.

Less than a dozen of the balck mayors preside over cities with populations of 100,000 or more, according to a survey complied by the black-oriented Joint Center for Political Studies here. More than half the black mayors represent towns that have population of 2,000 or less.

These were the mayors who came to Washington - which also has a black mayor - yesterday. "We're not satisfied with what's happened in the boondocks," said Prichard, Ala., Mayor A. J. Cooper, the organization's president. "We know that more has to be done."

Many of the black mayors are new to the political process, Cooper said, and come from places where there is scant potential for increasing city revenues because there is little industry to tax and few places for people to work.

The only way the mayors can restore their often delapidated housing stocks, build new city halls - in some instances for the first time - and meet the continuing demand for city services is to turn to the federal government, Cooper said.

Washington is the place from which federal monies flow, and that was one reason why it was chosen as the conference site, Cooper said. But as the mayors spent the first day of the conference in introductory sessions and touring the city, it also became clear that this city of 702,000 also held a symbolic importance as a showpiece for black visibility in government.

The visitors were shown several large District of Columbia and metropolitan regional facilities, some of whose operations are supervised by blacks. After a visit to the city's 152-acre wastewater treatment complex at Blue Plains, which is under the supervision of D.C. Director of Environmental Services Herbert L. Tucker, a black, one mayor remarked. "It sure is nice to see something this big that's being run by a brother."

The three-day conference agenda also includes appearances by and awards to some of the most prominent blacks in the Carter administration.

Although the mayors have not passed any formal resolutions. Cooper said he expected organizational stances on a wide variety of issues before the meeting at the Sheraton Park Hotel concludes Saturday.

These include an "energy stamp" program for poor people, ratification fo the Panama Canal treaties, and trade embargoes against South Africa, and more public works programs, and more employment and federal aid programs that owuld assist small cities. Most of the present urban aid programs are weighted toward larger cities, Cooper said.