Eighteen months ago, while he was stationed at Fort Riley, Kan., Army private Michael Rossier volunteered for a transfer to the nation's capital.

"i knew living here could be more expensive, but there's a lot of prestige associated with an assignment to Fort Myer," said Rossier, 21, who works as a motor pool mechanic at the Army post five minutes from the Pentagon.

Now, he's sorry he ever left the Midwest.

Rossier, who can barely afford the one-bedroom apartment in Arlington he shares with his 20-year-old wife and their infant daughter, is one of an estimated 28,000 enlisted servicemen financially squeezed by a tour of duty in the high-priced and housing-pinched Washington area.

Although senior bureaucrats, diplomats and military officers often view a Washington assignment as a political plum or a necessary step on their career ladders-"punching your ticket," as it is called in the military-many officers are not overjoyed at the prospects of a tour here either.

"Hell, I could move back to Fort Benning, Ga., and get an instant 25 percent raise just because it's so much cheaper to live there," said one Army lieutenant colonel stationed at the Pentagon.

For lower-paid enlisted personnel, the area's rapidly rising cost of living and rapidly disappearing supply of cheap housing dull the glow of Washington duty even more.

"If we'd stayed in Kansas, we'd we living on base and could afford a new car instead of having to keep our '69 Chevy," said Debbie Rossier, whose husband's basic Army pay of $6,144 last year put them below the Washington region's poverty level for a family of three.

Instead the Rossiers find themselves trapped by their present assignment, ranking too low to qualify for the area's limited base housing and making too little money to rent housing equal to what they could have had in Kansas.

The Army says it has only 357 housing units for enlisted families in the Washington are but all the units are reserved for career personnel who rank higher and make more money than Rossier.

The Rossiers receive a $150 monthly housing allowance, but the cheapest housing Michael Rossier could find was a $220-per-month apartment in the Lee Garden complex across Arlington Boulevard (Rte. 50) from Fort Myer. The $20 per month the couple says they have left after meeting their basic living costs must be stretched to pay for gasoline, car repairs and clothing for their seven-month-old daughter.

"A baby costs a lot more than you think at first," said Debbie Rossier. They have borrowed to meet their living expenses and still owe about $400 to friends and a credit union.

While the Rossiers came willingly to Washington, many enlisted people do so under protest. "We didn't want to come to Washington," recalled Velma Cross, whose husband Donald, a Navy yeoman (clerk-typist) with 16 years service, was transferred here from a Naval Air Station at Patuxent Rive, Md. "People like us just don't have enough money to live on."

The Defense Department has recognized the problem and officials say the Carter administration will ask Congress later this month to approve a variable housing allowance for the military. If approved, military personnel assigned to high-cost areas in the continental United States would receive higher housing allowances. Currently, only personnel assigned to Alaska, Hawaii and overseas are entitled to extra living expenses.

In its 1978 report, the Presidential Commission on Military Pay found that "the most egregious inequity" in the current military pay system is that "service members assigned involuntarily to high-cost-of-living areas suffer undue hardships."

Because of this area's high ratio of enlisted personnel to officers - 1 to 1 versus 15 to 1 in other areas, according to a Defense Department spokesman - many enlisted people here complain that their jobs are menial and undervalued.

An electronics specialist who is a communications chief at Fort Sill in Oklahoma, for example, might find he is only one of a large pool of technicians at the Pentagon. Particularly in demand in Washington are medics, drivers and clerk-typist like Cross, whose wife describes him as a "glorified secretary."

"There's a lot of depression and anger among enlisted people because they feel the jobs they're doing are [minial] and not the ones thay signed up for," said one social service aide who works with enlisted families. "The compalining about an 'erosion of benefits' is a way of coping with the feeling of not having any clout."

Velma Cross agrees that enlisted families often feel powerless, particularly when faced with unwanted transgers.

"A lot of people cry and scream and give all sorts of excuses," said Cross, a former president of a Navy wives club. "But if the Navy says you're going to Washington, there's no choice unless you get out of the service.

The Crosses said they have invested too many years in the military to quit before Donald Cross is eligible for retirement and a pension at age 40, after 20 years service.

The Rossiers fell differently and Michael Rossier, who grew up in Phoenixville, a town of 14,000 outside Philadelphia, said he is not planning to reenlist. "I make a lot more money on the outside as a mechanis," he said.

Military personnel officials who make assignments say they try not to transfer junior enlisted personnel like Rossier - whose basic pay after two years' service is about $500 per month - to Washington.

"We try to consider geographic preferences," said Army specialist Lloyd Meacham, "but the needs of the service come first."

Velma Cross, who like her husband is from a small town in West Virginia, remembered the summer three years ago when the family piled into their maroon van and drove the 120 miles each weekend from St. Mary's County, Md., to search for housing.

"Because my husband was going to be working at the Navy Recruiting Command in Arlington, we wanted to live in Virginia, so every weekend we drove all over the place looking for an apartment," said Cross, whose family was previously stationed in Northern Ireland charleston, S.C.

"We would have liked to but or rent a house but with what my husband makes [real estate agents] looked at us like we were crazy," Cross recalled. The average home in Arlington is valued at $73,000, county officials say.

After a three-month search, the Crosses found a three-bedroom, $315-per-month apartment in Fairfax County. After a year on the waiting list, they moved into a four bedroom town house at Bowling Air Force Base in Southeast Washington.

Rent and utility costs for the comfortable house, one to 1,400 on the base available to Navy and Air Force personnel, are paid from the $213 monthly housing allowance Cross receives.

"It seems like we have less and less all the time," said Velma Cross, whose husband earned $10,186 in basic pay last year.

As do all enlisted personnel, Croxss recives a clothing allowance of $7.40 per month to cover the cost of the uniform he is required to wear once a week. That did not cover the several hundred dollars of civilian clothes he had to buy when he came to Washington, In Patuxent, he wore a uniform to work every day.

"We'd like to send our kids to private school but we can't afford it," said Velma Cross, whose three sons attend public schools in Anacostia. "We don't feel it's fair to be stuck in an area where you have that additional expense. A lot of wives [at Bolling] work just to pay tuition.

Some congressional staff members familiar with the military pay system say that families like the Crosses are far better off than a $10,000 salary would indicate.

Unlike civilians who must "live on the economy," military families receive free health care, enjoy substantial savings on food and consumer goods by shopping at special discount stores, and receive nontaxable housing and food allowances in addition to their basic pay.

Military pay critics point out that it would be virtually impossible to it would be virtually impossible to rent a modern, four-bedroom town house for $213 per month including utilities anywhere in the metropolitan area.

Martin Binkin, a senior policy analyst for the Brookings Institution and author of several books on military pay, conceded that any family in a situation like the Crosses' is in "tough shape." But Binkin said that many military families underestimate their benefits.

"You have to understand that the natural tendency of military people is to grouse," added Binkin, a retired Air Force colonel.

Military officials say that those least able to cope with the complexities and expense of Washington life often are the younger recruits from the rural South and Midwest, particularly those with young children.

"A lot of them are just overwhelmed," said Shirley Lester, director of the Fort Myer housing office. "They come here with no car, no furniture, and very little money."

"I remember one young couple who drove down from somewhere in Pennsylvania" said Lester, who has taken destitute families home with her for periods ranging from severals nights to several months. "The wife was 17 and seven months pregnant, and their old car had died somewhere enroute. They arrived with $100, which isn't enough for an [apartment] security deposit."

"What disturbs me most," said Lester, "are the [low-paid] young guys who don't have any kids and don't want their wives to work."

Escalating housing costs and the rash of condominium conversions in close-in once inexpensive areas such as Arlington have forced many families to live in such outlying areas as Woodbridge, Reston and Manassas.

"Then there's the problem and expense of commuting, which is compounded by the gas shortage," Lester noted.

Some enlisted families, including the Crosses, say that despite the financial pinch and the second job many are forced to take, they stay in the military because of the travel, the security and feelings of patriotism.

"Washington D.C. can be one of the best place in the world to be," said Velma Cross. "But you can't enjoy all the free things like museums if you're worrying about money all all the time." CAPTION: Picture, The Rossiers are below poverty level. By Margaret Thomas-The Washington Post