Young Americans are experimenting with drugs far more than their counterparts did in the heyday of the drug counterculture of the 1960s and early 1970s, according to a nationwide Washington Post-ABC News survey.

In the survey, half the people between the ages of 18 and 30 said they have tried marijuana and one in five said they have used cocaine.

By contrast, among those aged 31 to 44 -- people who came of age when drug use first became widespread -- only one third said they have ever used marijuana, and only one in 12 reported having tried cocaine.

Furthermore, while drugs started as a big-city problem a generation ago, the survey shows that marijuana and cocaine use have spread widely, like clothing styles, to the nation's suburbs, small towns and rural communities.

Drug use is still highest in the big cities, and along the East and West coasts. But it has risen sharply everywhere else.

In addition, many young people, unlike their elders, want to see marijuana use made legal.

Among those aged 18 to 30, four in every 10, whether they use the drug or not, feel there should be no penalty for possession of small amounts of marijuana for personal use, according to the Post-ABC News poll. Among those over 30, only two in 10 say it should be legalized.

There is virtually no support in either group for legalization of cocaine, with 9 percent of the young and 5 percent of older citizens saying they approve.

Young people, by 47 to 37 percent, tend to see alcohol as causing more problems in their communities than drugs. Older Americans are more evenly divided, with 34 percent saying drinking is a bigger problem where they live, and 35 percent saying drugs are a bigger problem.

Both groups, however, say that drinking has created more grief in their personal lives than have drugs. Asked whether drinking has "ever been a cause of trouble in your family," one of every three people interviewed, regardless of age, said yes. Sixteen percent said it had caused "a great deal" of trouble.

Less than one person in 10 said drugs have caused trouble in their families, with 4 percent saying they have caused a great deal of trouble.

Only 3 percent in the survey, in which 1,503 people were interviewed from May 9 to May 13, admit to current use of illicit drugs. That suggests, for one thing, that while many people may experiment with drugs, relatively few stay with them.

But it also suggests that the poll understates the amount of drug trafficking taking place. It seems certain that some drug users, perhaps a substantial number, are simply not about to admit to an interviewer on the telephone that they are breaking the law by using cocaine or marijuana.

For the same reason, figures on experimentation may also be understated, although probably not to the same degree.

However, there is no reason to suspect that older people are lying to pollsters substantially more than younger ones. Thus, taking all age groups into account, the survey shows a great many young people dabbling in area that is foreign to most of their parents and almost totally unknown to their grandparents.

Among those in the survey who are 61 or older, only 2 percent say they have ever used marijuana and 1 percent say they have used cocaine. Only 1 percent in that age grouping say they use either drug frequently, and only 3 percent say they have friends who use them.

Similarly, among those aged 45 to 60, only 8 percent say they have tried marijuana and 3 percent say they have used cocaine. None admit to being frequent drug users now; only 3 percent say they use them occasionally. But among this group, 20 percent say they have friends who use either marijuana or cocaine.

Among people between 31 and 44 years old, 34 percent say they have tried marijuana and 8 percent have tried cocaine. Four percent say they are frequent or occasional users, and almost half -- 44 percent -- say they have friends who use one of the drugs.

As for those aged 18 to 30, 49 percent say they have used marijuana, 20 percent say they have used cocaine and 8 percent say they currently are frequent or occasional users of one of them. Two of every three say they have friends who use one of the two drugs.

Among these young people, men and women report having experimented with marijuana to about the same degree. But men are more likely to have tried cocaine, and are also more likely to be using either of the drugs today.

In the 18- to 30-year-old age bracket, 53 percent of the men interviewed and 47 percent of the women say they have used marijuana in the past. Twenty-five percent of the men and 16 percent of the women say they have used cocaine.

Twelve percent of the men in that age group but only 5 percent of the women admit to using mar- ijuana currently; for cocaine the figures are 5 percent among men and 2 percent among women.

There is some evidence, provided by the University of Michigan, that marijuana smoking among the young has declined slightly in recent years and that cocaine use has reached a plateau.

But even the Michigan researchers say that both drugs are used far more today than they were a decade or two ago.

Comparisons between generations reveal how dramatically the drug problem has grown, especially in places that were the least affected not long ago,

Whether they have experimented or not, the great majority of Americans want a strong national campaign to cut off drugs at the source. One third in the survey take the view that "convicted heroin dealers should get the death penalty."

Seventy-eight percent of all people interviewed, including 63 percent of those who say they have used marijuana or cocaine, agree with the statement that "the U.S. government should spend as much money as necessary to stop the flow of drugs into this country."

However, the great majority also doubt that such a campaign would be successful. Eighty-four percent also agree that "drug abuse will never be stopped because a large number of Americans will continue to want drugs and will be willing to pay lots of money for them."

The public also endorses strong alcohol abuse measures. By 79 to 19 percent, those interviewed endorse legislation that would raise the legal drinking age in all states to 21, a measure aimed at reducing teen-age drunk driving. Congress has ruled that by 1987, states that allow sales of liquor to people under 21 will risk losing federal highway funds.

By a slim majority of 51 to 47 percent in the poll, the public feels police should be allowed to stop motorists at random and give them breath or coordination tests, regardless of whether they have been driving erratically.

There is less support for two other measures aimed at cutting down drunk driving. By 63 to 33 percent, the public disapproves of making bartenders and bar owners liable if someone leaves their establishment drunk and kills or injures a person in an auto accident. Similarly, by 66 to 31 percent, those interviewed oppose making homeowners liable under similar circumstances.

But by 56 to 43 percent, a majority favors taking away the license of a drunken driver on the first offense, regardless of whether he or she is involved in an accident.