An unprecedented rental housing crunch is making it increasingly difficult, if not impossible, to find an apartment in the Washington area, and tenants lucky enough to have a place are facing skyrocketing rents, according to a new federal study.

The rental housing shortage, according to the study, has been caused by a "dramatic" surge in population and the conversion of thousands of apartments to condominiums over the last five years.

The tight market, which is especially acute in Northern Virginia, was blamed for a 10.6 percent jump in rents last year, a figure more than double the 1984 inflation rate.

The study, prepared by the Department of Housing and Urban Development's Washington regional office, is the first to survey the area rental market since the 1980 census. The report is not yet public, but a copy was obtained by a reporter.

"The situation is difficult for a lot of new rental households. Even those who have been in the market for some time are seeing accelerations in rent that have never occurred before," said Arthur D. Goldstein, HUD regional director of economic and market analysis.

Since the 1980 census, 12,598 new apartments have been built in the metropolitan area. But that construction has not offset the loss of 24,230 units to condo conversions. As a result, the area's apartment stock fell from 503,602 units to 494,302, for a loss of 9,300 units, the study states.

While the number of apartments was declining by 1.9 percent, 94,400 people moved to the area, causing the population to climb by 3.2 percent. The "two conflicting factors" produced the tight market, the study said.

The vacancy rate -- the number of units available to rent at any given time -- reflected the trend, plunging from 5.4 percent in 1980 to 2.1 percent this year. Ideally, the rate should be 6 percent, according to the report.

Although Washington went through a similar rental housing shortage in the late '70s, the current crunch is considered worse, because the population is increasing and because high interest rates are making it harder to buy a house, Goldstein said.

The shortage is particularly severe in Alexandria, which has lost 1,700 apartment units, or 5.5 percent of its rental stock, since 1980. Its vacancy rate has fallen to 1.1 percent, a level that means apartments essentially are unavailable, according to housing experts.

The rest of the Virginia suburbs -- Arlington, Fairfax, Loudoun and Prince William counties -- are in the same straits. Vacancy rates range from 0.3 percent in Loudoun to 2.1 percent in Fairfax. Overall, the rate is 1.7 percent, according to the study.

The Virginia suburbs lost 5,450 apartments, while population surged by 75,500 residents. Most of the growth occurred in Fairfax, which lost 2.7 percent of its rental housing as population rose by 53,200, or 8.9 percent.

In Maryland, Montgomery County gained 24,900 residents and 3,250 new apartments, despite the loss of 3,470 units through conversions. The vacancy rate, however, still declined from 5.1 percent to 2.6 percent.

Prince George's County gained 9,300 residents, but lost 2,550 apartments. Its vacancy rate fell from 5.9 percent in 1980 to 2.7 percent in 1983, the latest figure available.

The District lost 15,300 residents, or 2.4 percent of its population, while its apartment stock fell from 163,297 units to 158,747 units, also a 2.4 percent decline.

Athough 2,587 new apartments were built in the District, 7,140 others were converted to condominiums, for a loss of 4,553 units. The vacancy rate declined from 6 percent to 2.4 percent.

"This shortage of rental units is causing serious problems for those seeking rental housing," the study stated.

"Not only is . . . the rental market making it difficult for households to find available apartments, but this shortage is causing monthly rental rates to rise at an accelerated rate," the study added.

In Alexandria, for example, overall rents increased by 18 percent, from $422 a month in 1983 to $498 last year. But rents for two-bedroom apartments, normally the most sought after, jumped by 21.6 percent, from $459 to $558 a month.

In contrast, rents increased by 8.8 percent in Montgomery County and by 8.4 percent in Fairfax County.

"It's basic economics," said Goldstein. "When you have a limited supply of apartments, rents go up."

The tight market conditions are making it extremely difficult for moderate- and low-income families to find housing, according area housing officials.

Even families that qualify for federally subsidized housing are suffering, because most rents in the area exceed ceilings set by the Reagan administration under the federal Section 8 housing program, officials said.

Under the program, low-income families pay rent equal to 30 percent of their monthly income.

The goverment pays the rest, but only up to a federally determined "fair market" amount.

"The combination of rising rents and Reagan administration efforts to hold down rent ceilings is causing problems," said Richard Farrara, director of housing and community development in Montgomery County.

Condominium conversions reached record highs in 1980 and '81. But since then, declining interest rates and an "over-all improvement in the home-buying market" have sharply reduced the trend, the study notes.

Of the 31,600 units that were converted to condominiums during that time, 7,400 are occupied by renters. The study estimates that 15 percent of all new condominiums built in the Washington area also are renter occupied.

The study did not take into consideration apartment demolitions, coop conversions, condominium reversions to rentals and town houses and detached home rentals.

New apartment construction was outstripped by conversions from 1980 until 1982, but over the past two years, the trend has reversed. Apartment construction exceeded conversions by 2,386 units.

The number of building permits issued for new apartments was higher during the first 10 months of 1984 than at any other time since 1977. But the number of permits for subsidized units fell to a 15-year low, the study found.

Whether both trends will continue is subject to debate. Tax proposals under consideration by the Reagan administration will limit the use of mortgage revenue bonds to finance apartment construction and may limit investments in rental housing by syndications. The two have been the driving force behind the recent spurt in apartment construction, officials said.

The Reagan administration is conducting and experimental program to replace Section 8 housing certificates with rent vouchers. No funds, however, have been included for the program in next year's federal budget, said Farrara, whose agency is participating in the experiment.

"Is housing under attack on all fronts? The answer is yes," Farrara said.