The Department of Housing and Urban Development awarded 3,000 housing vouchers worth $52.8 million to 41 small cities and rural communities this week for a test of the vouchers' effectiveness in providing shelter for low-income families. The recipients included public housing agencies in Fairfax, Charles and Anne Arundel counties.

HUD Secretary Samuel R. Pierce Jr. said vouchers will enable the government to "do more with less" money, chiefly because no new construction or rehabilitation of public housing is needed. Families using vouchers find their own housing in a community's existing stock.

Pierce said he "eventually wants to have the vast majority" of the agency's housing assistance in the form of vouchers.

The Fairfax Department of Housing and Community Development was given $2.37 million to provide five-year vouchers for 125 households. Anne Arundel and Charles counties received $1.99 million for 100 families and $1.3 million for 70 families, respectively.

The vouchers will go to families whose incomes are less than half the median for the areas where they live, meaning that Fairfax residents with incomes under $17,900 will be eligible. A voucher will cover the difference between 30 percent of a family's income and the area's fair market rent, which is established by HUD.

A family that wishes may spend more than 30 percent of its income for rent, a choice not open to families using the Section 8 subsidized housing certificates HUD wants to get rid of. A family lucky enough to find a home for below-market rent, however, can pocket the difference. The Section 8 program also prohibits participating property owners from charging more than market-rate rents, a restriction that is not present in the voucher regulations. Critics have predicted that this aspect of the voucher system will lead to rent gouging.

Last July Pierce announced the awarding of 4,543 vouchers for trial programs in 20 larger cities and states, but the first vouchers are just now being given to families. Montgomery County, which will get 182 of the vouchers, expects to issue the first ones to needy families next month, said Mary Jones of the Montgomery Housing Opportunities Commission.

The present assisted housing programs that "rely on new construction or substantial rehabilitation are . . . both inefficient and enormously expensive," Pierce said at a press conference this week. Vouchers are the substitute, an idea growing out of a Rand Corp. study showing "there was no shortage of rental housing nationwide . . . although there were shortages in some communities . . . ," he said.

Fairfax is one of those areas where the shortage of affordable housing for the poor is critical, according to Virginia Johnson, a spokesman for the county's housing and community development department. More than 3,700 families, most with incomes less than half the county median, are on the waiting list for homes, with the average wait more than two years, Johnson said.

Much of Fairfax's rental stock has been lost to condominium conversion, and there is little development of multifamily housing, she said. Under these conditions "we realy don't know whether families will be able to find places" with the vouchers. "But the need is so great we're willing to give it a try," she said.

Previous trials in some areas of the country have shown that even in communities where shortages exist, people who persist usually can find housing, said June Q. Koch, HUD assistant secretary for policy development and research. In addition, "our whole . . . strategy" for housing the poor depends on construction by private builders, Koch said.

In an effort to spur developers to build more housing, Pierce has negotiated successfully with the Treasury Department to retain builders' tax benefits that would have been eliminated in Treasury's original tax bill, Koch said. "He got the rents down from 40 percent to 20 percent," she added, referring to estimates by the home building industry that rents would rise by as much as 40 percent to cover increased costs resulting from the loss of tax breaks. "The secretary felt that was still too high, so he has appealed" for more concessions to brink the figure down to 14 percent, she said.

The estimates, made by the National Association of Home Builders, have been viewed skeptically by many in the industry. The skeptics point out that if the market could bear rents 40 percent higher, property owners already would be charging that much.