Thousands of Northern Virginia teen-agers are out of work this summer because there simply are not enough jobs to go around.

"I think it's possible there are more kids unemployed this summer [than there are employed]," said Gary Post, employment director for Alexandria. "When you think about that, it is pretty heavy-hitting social concept. Our youth are willing to work; we have nothing to give them."

Post and other Northern Vvirginia officials say this may be the toughest year yet for teen-agers who want to work. The officials report hundreds of applications for few job openings, and many teen-agers say they have pounded the pavement for weeks without success.

The result, local officials and teen-agers say, is a lot of frustrated kids with not much to do but hang out.

One place the kids are hanging out is the Pinball Eatery in Arlington. One recent afternoon, a visitor found dozens of teen-agers playing dozens of video games.

"Unemployed teen-agers? I got 'em," said owner Harold Dickerson as he untied his apron and pulled up a stool at the food conter. "Maybe 150 a day come in with no jobs and nothing to do but play pinball, drink Cokes and beat the heat. They put their money into the games, then ask me for work for more money to put in the games."

Dickerson said he has tried to give the youngsters some jobs around his store -- sweeping out the back, washing windown, taking out trash -- to give them a few dollars. Most of the time, he said, the money never leaves his establishment.

"I was thinking of hiring a teen-ager for the summer but I looked at my taxes and figured I just couldn't afford it," he said. "These are good kids. They really want to work. It's just [that] there are no jobs."

Chris Selb, a 16-year-old from Arlington, has been looking for a summer job since spring. He has applied at drugstores, groceries and fast-food restaurants, but with no luck.

"It's very frustrating because I want to work and I could work okay," he said. "There's nothing. Maybe one in two of my friends found jobs."

Mostly, he says, he has been hanging out this summer and attending a driver's education course in the evenings. Neighbors pay him to mow their lawns or do odd jobs, but the work is far from steady.

His father, John Selb, sympathizes with his son's frustrations over the lack of work.

"Chris is very interested in sports," he said. "I know he'd like the money for sports [equipment] and to save for college. His dream is to go to Notre Dame. He wouuld make a fine worker. There are just no jobs to be had."

Northern Virginia employment officials say that this year the number of youngsters seeking work has far outpaced the openings available. In some cases there have been eight applicants for each opening, they report.

In March, Fairfax County held a job fair to recruit teens for 50 summer jobs in county parks, recreation facilities and the public works department. More than 400 youngsters turned in applications, according to Rita Kayn, a personnel analyst for the county. The Comprehensive Employment and Training Act (CETA) office in Fairfax, which places lower-income teens in jobs in federal and nonprofit agencies, received 1,500 applications for 350 jobs, according to officials there.

In Arlington, budget cuts in CETA meant reducing the program by a third from last year. And program director Jerry Gordon said more than 600 youngsters applied for the 296 CETA positions open this summer.

Alexandria had 243 city jobs this year, only a few less than last year. The big difference was that more than 1,000 applicants were seeking those jobs, according to Post.

Jobs with private businesses were equally hard to come by, according to Northern Virginia officials.

"Summer jobs in the private sector are scarce this year with the general economic malaise," said Alexandria employment director Post. "When you combine that with less CETA, fewer jobs in county and town governments, you've got real problems."

Last spring, officials of the Summer Youth Employment Program, a federally funded agency set up to match teens with jobs in private business, sent out a flyer asking firms to register with the agency i they had jobs available.

Regional Directory Wesley Caison said the program was able to place 450 youths in jobs in Arlington and Alexandria. But that hardly met the need: More than 1,000 youths applied for those 450 spots.

The Arlington Chamber of Commerce, which conducted a similar program, was able to place 30 youths with private firms, according to Bob Reade, executive vice president of the chamber. More than 200 youngsters applied for the jobs.

A spot check in Fairfax, Alexandria, Arlington and Falls Church found that most supermarkets, drugstores and fast-food restaurants, traditional bastions of summer jobs, have unprecedented numbers of applications but fewer jobs available.

Safeway spokesman Ernie Moore said the supermarket chain had 200 applications for summer jobs in Northern Virginia, but had only 15 openings, three fewer than last year.

John Esher, who owns a Baskin-Robbins store in Falls Church, said he has received 150 to 200 applications since May for summer jobs, but he is not hiring. "My employes work here through the year," he said. "I don't hire extra for the summer. I just increase their hours."

A Roy Rogers restaurant in Alexandria receives 15 to 20 applications a week, according to manager Hakan Yavalar, but the restaurant isn't hiring.

"Nobody is," Yavalar said.

John Gichuru, 16, of Arlington, said he applied at 70 places after he returned from private school in Connecticut at the beginning of the summer. "They just took my application and gave me the runaround," he said. "There aren't any jobs anywhere. Even my mother told me not to get all upset about it."

Regina Smith, 17, of Arlington, said she has searched everywhere for a summer job. She is taking two classes this summer in an adult education program while she continues to look for part-time work. During a break from her class at the Langston Community Center last week, she said she could use the spending money she would earn from a summer job and would like the experience.

"The whole thing is just pitiful," she said. "Right when jobs are real scarce in the restaurants and stores that man [President Reagan] turns and cuts the summer job programs."

In the competitive summer jobs market, college students often have first crack at the good jobs because they get out of school earlier, usually are more experienced and often know the right people, according to Alexandria's Post. And more affluent teens, he said, are in a better position to get the few summer jobs because they have better access to transportation.

"But no matter what income group, it is very frustrating to a young person who wants to work not to be able to find work," said Post. "Summer jobs mean spending money, responsibility, savings for college, something to look forward to. Instead they're just hanging out, feeling left out."