Until a teen-age alcoholic hits rock bottom, there is little chance of convincing him that his drinking problem is serious enough for treatment as drastic as hospitalization.

For Aileen, 17, the realization came after a lengthy period in which she would drink a quart of beer "just to get started in the morning" and then down large quantities of vodka later in the day. After she was expelled from school, was caught pawning her parents' silver and thrown out of the house onto the streets of Arlington with no place to go, she said she knew she couldn't take any more.

Michelle, 17, said she stole her father's car, skipped class at her Fairfax County high school and got drunk with a friend one day last February. "I was driving in a blackout when a van struck me in an intersection and knocked the car 45 feet in the air, knocking me unconscious and spilling beer all over. . . . I then decided I had a slight problem with alcohol and needed to help myself out."

Jenny was 13 when her parents discovered she drank vodka from a jar in her purse on the way to her Arlington junior high, and was also into pot, speed and Quaaludes. She said the morning her parents found her roaring drunk they finally admitted she needed help.

For these teens, their personal nadirs jolted them to a painful realization that their drinking had gone so out of control that hospitalization and intense therapy offered the only way out. For help, they turned to one of several Northern Virginia facilities that run intensive treatment programs for adolescent alcoholics.

"We get the kids who drink everyone under the table," said Patricia H. Powers, program director of the adolescent unit at Arlington Hospital's Alcoholism Treatment Program, the largest such unit in Northern Virginia. "Kids begin to test themselves in their teen-age years. It's a creative time and an intense time. Add alcohol--and maybe drugs--to the tension of this age, and you get a double-headed monster."

The unit treated 150 teens ages 13 to 18 last year, but officials know that is only a small segment of the area's young alcoholics. With only eight beds available to the teen-age program, there is usually a waiting list.

"The problem is in epidemic proportions," said Dr. Anthony H. Rapone, director of treatment for the Arlington program. He estimates conservatively that one of every 10 teen-agers who drinks is an alcoholic.

Virtually all teen-agers with severe drinking problems are also drug users, Rapone said. The Arlington unit concentrates on patients whose "drug of choice" is alcohol, though they counsel patients to lead alcohol- and drug-free lives.

Springwood, a private psychiatric hospital on a 45-acre estate in Leesburg, specializes in dual addictions. They treated 36 teen-agers with combined addictions to drugs and alcohol last year, and 22 so far this year. "What usually happens when kids' drug sources dry up for a while is that they go to the bottle," said Tricia Christian, Springwood's director of public affairs. "They substitute whatever is available."

Not every teen-ager with a drinking problem needs hospitalization. For some, private or government-sponsored outpatient therapy and counseling, combined with help from Alcoholics Anonymous chapters, can supply the needed help. Inpatient programs are for the hard-core drinkers--those who have reached a certain limit and are ready to admit their desperate need for help.

That cry for help may come after a devastating incident. Former patients recount stories of driving a family car through a window at Tysons Corner, getting caught stealing a case of beer from a 7-Eleven store or throwing a dining room table at their father and not remembering it.

Patients come from all segments of society, Powers said, but the majority are from white, middle-class families. She said statistics have shown that a teen-ager's risk of becoming an alcoholic is four times greater if one parent is an alcoholic, and the likelihood is six times as great if both parents are alcoholics.

Youths admitted to the treatment unit must conform to a tough regimen--from 6:45 a.m. until 11 p.m.--crammed with counseling sessions, individual and group therapy, recreational activities and lectures on nutrition, drugs and drinking. The teen-agers stay in standard hospital rooms jazzed up with brighter furnishings.

Springwood has a sylvan setting that permits more outdoor activities. The teen-age patients' 16-hour days include counseling and lectures plus classes in leisure-time activities such as pottery and horticulture--"so that when they are alone, they will find something to occupy their time to keep them away from alcohol and drugs," said Springwood administrator Donald McArthur.

For the first few days, patients go through detoxification, a period during which the body readjusts to the abscence of alcohol and/or drugs, and patients may experience hot and cold shakes, headaches and occasional hallucinations, according to Dr. Warren P. Klam of the Arlington unit.

"At first, it was really hell," said Phil, 18, who has spent two sessions at Springwood. "The first thing I wanted to do in there was get high."

Most patients in the Arlington program take antabuse, a chemical that induces nausea if the recipient drinks. The teens often continue taking antabuse after leaving the program to help them them through slippery times when strong peer pressure might lead them to drink.

Doctors also place strong emphasis on health education. "Kids don't want to look ugly, get pimples, have their hair fall out or get fat," said Powers. "They don't want to lose their sexuality. Concern about health is a strong force with them--much stronger than with most adult alcoholics."

A Fairfax County youth who used to drink 13 beers at a sitting before going through the Arlington program said doctors there told him he "had gastritis, hepatitis, fatty liver--and that I might not live past 20 if I continued like that."

"All that hit me hard, especially the fact that I was an alcoholic and really sick."

Both Arlington and Springwood take their teen-age patients to Alcoholics Anonymous meetings almost daily and urge them to attend as often as possible after they leave the hospital. "I go to an AA meeting every night," said 13-year-old Jenny. "All my friends are there now. I think I will have to go the rest of my life."

Hospitalization treatment programs cost about $6,500 for Arlington's 28-day session and $19,500 for six weeks at Springwood. Hospital officials say most patients' health insurance policies cover from 80 to 100 percent of the charges.

The Arlington unit claims a 62 percent success rate in abstinence from drugs and alcohol, somewhat lower than the 80 percent rate for their adult patients. Officials at Springwood estimate an 83 percent success rate. Both facilities monitor teenagers' progress with after-care programs that last as long as one year.

But, as the Arlington brochures say, "the hard part comes after the detox" when the teen-agers return to their families and friends and are faced with deciding whether to drink or not. Some change their social lives completely and spend their time exclusively with people they've met through AA; others get on a roller coaster of drinking, quitting and drinking again.

"I don't hang out in bars now," said Craig, a Leesburg 19-year-old who left Springwood 15 months ago. "I have a hard time comprehending social drinking. I always drank to get drunk, and I can't comprehend someone taking two drinks and stopping."

"All my old partying buddies are out of my life now," said Phil, who has been sober for almost a year. "That is a slippery spot for me. At this point of sobriety, I feel uncomfortable going around people who drink. But I go to a lot of sober parties and they are tons of fun--and this time I can remember it."