Fairfax County's emergency housing shelter is another way station for Sharon Hudson and her two sons in their search for an affordable place to live.

For 16 months she has lived from a suitcase, shuffling between rooms in private houses and shelters -- 19 in all. This nomadic life was forced on Hudson when she slipped down 12 steps in a January 1984 ice storm, cracking her ribs. Disabled, she lost her $5.25-an-hour job as a computer operator for Computer Science Corp. in Maryland and then lost her apartment.

Since that fateful day, Hudson has exhausted her savings, overstayed her welcome with friends and family and filled out so many rental applications she has lost count.

"It's frustration all the time. It's turmoil. You go knocking on doors and they say 'no kids,' 'adults only,' or they say you don't earn enough."

With 14 years of experience as a computer operator and school-bus driver, Hudson is anxious to get back to work, but first she wants a roof over her head. Her social worker, Roma Olin, said that unless someone sublets her a cheap room in his or her house, it will be virtually impossible to help Hudson and her two sons, one aged 5, the other 6 weeks old. Her only income now is a $366 monthly welfare check.

Hudson is one of the estimated 6,500 low-income people in Fairfax County seeking housing assistance who have become the focus of mounting public concern over housing shortages.

The Federation of Citizens Associations and the League of Women Voters are lobbying the Fairfax County Board of Supervisors to allocate more money for housing programs.

The Northern Virginia Board of Realtors, the Northern Virginia Builders Association and Fairfax County Chamber of Commerce have joined forces to urge the county to ease its building regulations. Developers and builders promise to build more low-cost housing in return.

In response, the Republican majority on the county's board of supervisors is calling for the private sector to help solve the housing crisis. The board this month is expected to name a joint task force of public- and private-sector representatives to study ways of increasing the housing supply for the working poor.

The housing programs traditionally are unpopular in a county where the median family income is $51,100. But today there is unanimity among officials and industry groups over the need to help low-income renters.

Figures compiled by the county's office of research and statistics show that multifamily rental units have declined from 35.8 percent of the total housing stock in 1970 to 16.6 percent today. At the same time, rents have been spiraling upward faster than inflation. In 1977, a renter could expect to pay $251 a month for the average unit; the same unit by 1984 cost $466, county statistics show.

And competition for those 46,939 multifamily units on the market today is fiercer than ever before. Forced out of the home purchase market by rising prices, more middle-income people are competing for this declining stock of rental units, according to a report by Real Estate Research Corp.

The rental vacancy rate now is about 2 percent, which means the market is extraordinarily tight, said Deidre Coyne, information officer for the county's Redevelopment and Housing Authority. A healthy vacancy rate is considered to be 4 to 5 percent.

Subsidized housing no longer can pick up the pieces, Coyne added. Under the Reagan administration, federal funding for public housing has been cut, forcing people onto an ever-growing waiting list for the Section 8 rental subsidy program and public housing. The housing authority this month was forced to close its lists to new names because it already has a 2 1/2-year backlog. Hudson, for instance, signed up for assisted housing last fall but can expect no help before 1986 or 1987, Olin said.

Desperate for anything, at least 31.4 percent of the county's renters are paying more than 30 percent of their income in rent, Real Estate Research Corp. stated in its 1983 report on Fairfax County's housing needs. Unless the county intervenes, the proportion is expected to rise over this decade, the report warned.

"We've got to involve the private sector in finding solutions to these problems, and there's no precedent for that approach," said County Supervisor Thomas Davis III, the new Republican chairman of the board's housing subcommittee.

One idea he wants to explore is providing incentives to developers and builders to construct more low-income housing. For example, the county could speed the review process for building applications, allow higher density development and expand the use of tax-exempt financing for multifamily projects if the development community would set aside a percentage of the units for low-income residents, Davis said.

Changes such as these could help reduce the cost of a new town house by 12.6 percent, Real Estate Research said in its report. Davis wants to ensure these savings are passed on to the consumer.

Davis is wary of 1970s-style solutions to housing problems such as rental subsidy programs, preferring instead to concentrate on ways of increasing the stock of rental housing. However, he said he would consider a proposal to have the county purchase rental units that would be managed by the housing authority. The authority already has 883 public housing units.

But the proposal that appears to hold the most promise is higher density development.

"It's not even debatable. That is one of the most significant elements in making housing affordable," said Willam L. Berry, former president of the Northern Virginia Builders Association.

NVBA cites a Department of Housing and Urban Development demonstration project on ways to reduce housing costs. An experiment in Phoenix found that $3,676 per unit could be saved in a 255-home subdivision by increasing the density -- more money than could be saved through faster processing of building applications or cheaper construction techniques. The project used smaller street widths, curbs and driveway entrances, and clustered units around courtyards to reduce utility line runs, leaving room for an extra 60 homes.

County Supervisor James M. Scott agreed that higher density provides the only significant saving for the developer but warned, "It's a pretty sensitive issue." Because citizens oppose moves to rezone land in existing neighborhoods for multifamily units, Scott expects higher density projects will be located in new developments.

Today there are 456 acres of land planned for 20 units or more, 0.19 percent of all the developable land in Fairfax County, according to county statistics. County Planner Richard G. Little is surveying the county to find additional land suitable for high-density homes.