The government's housing voucher demonstration program, approved by Congress amid much controversy in 1983, will come up for renewal this year without having demonstrated anything: the Department of Housing and Urban Development has yet to get funds out to housing authorities.

In Montgomery County, listed with much fanfare last year as a test area, Mary Jones of the county's Housing Opportunities Commission, said an application was submitted to HUD in August and she went for training; but since then, nothing has happened.

Congress appropriated $86.4 million in the fiscal 1984 budget to finance trials of the housing vouchers in 20 cities and states. Under the program families can shop for their own houses or apartments in any area they like, pay 30 percent of their income for rent and HUD will pick up the tab for the difference between that sum and the fair market rent. Recipients can pay more than 30 percent of their income for rent if they choose, an option not available under the Section 8 rental assistance program the vouchers are designed to replace.

HUD Secretary Samuel R. Pierce Jr. has said the vouchers will enable low-income Americans "to choose where they want to live and how much of their own income they want to pay for rent."

But the snail's pace of preparations for the demonstrations has irritated some in Congress. The housing bill that Rep. Henry B. Gonzalez (D-Tex.), chairman of the House housing subcommittee, has introduced contains no money for vouchers in fiscal 1986, which begins next October, in part because there have been no demonstration results to evaluate, said a subcommittee staff member.

"It's taking them HUD as long to get this thing rolling as it did the Section 8 program they're so . . . critical of," said a housing subcommittee staff member. The administration has touted the vouchers "since 1981 as so much better than public housing and Section 8, with less red tape. When they were making their case for the program they acted as if it would be ready to roll in a few months."

In the Senate housing subcommittee, however, there is considerable support for the vouchers, according to a subcommittee staff member. The time it is taking to get them started is within reason because HUD has been working on many programs, she said. The subcommittee staff expects a request for vouchers to be included in an administration housing bill this year, she added.

Administration sources said Pierce asked for funds for 100,000 vouchers for next year, more than double the number to be distributed in the trial programs this year. But the sources could not say whether the request will still be in the budget when the White House sends it to Congress next month.

The delay in getting the program underway is "purely procedural," said Hunter Bourne, HUD special assistant to the assistant secretary for housing. A new computer system to track the program had to be set up, and modifications in contract documents and financial forms had to be cleared with the Office of Management and Budget, he said. Time needed to select an independent company to monitor the program was another cause of delay, according to Bourne.

The voucher program has been controversial since it was first proposed early in the first Reagan administration. HUD considers it one of the most important new programs. Gonzalez says HUD's contention that vouchers will work is a "fairy tale."

He said that "25 percent of Section 8 certificates are returned unused because suitable and affordable housing isn't available," a percentage critics say could rise sharply when the vouchers are distributed. Under Section 8 landlords who participate in the program can charge only fair market rent, which is set by HUD. With vouchers, building owners can exceed the market rent, a provision some housing administrators said could lead to higher prices and rent gouging.

If, on the other hand, the tenant finds a below-market place, he can pocket the difference, creating what backers of the program call a shopping incentive.

Several Washington area jurisdictions report that a share of their Section 8 rental assistance certificates go unused because families can't find affordable homes. An Arlington spokeswoman said 80 of 620 certificates are not being used because poor families can't find apartments they can afford. Montgomery County has been able to use from 95 percent to 97 percent of its Section 8 certificates.

An Alexandria spokesman said from 35 percent to 40 percent of the city's eligible families fail to find an apartment where they can use Section 8 certificates. In the past, high prices have caused problems for Section 8 recipients in Prince George's County, but a recent increase in HUD's rent limits has eased conditions there, according to a spokeswoman.

Earlier tests of vouchers were carried out in 12 cities in the past decade, with results that were viewed differently by proponents and critics.

Montgomery County could start putting its 182 vouchers into the hands of home seekers within two weeks to a month after the HUD money is available, according to Jones, who is administrator of the Section 8 program.

There are 7,000 families on the Montgomery waiting list for assisted housing, she said.