Andrei Voznesensky describes the scene cooly, precisely.It is Moscow just a few months ago. He has arrived to be the featured attraction at a poetry recital: "A young woman pushed her way through the crowd on the street. There were tears in her eyes. She begged me for a ticket. In the hall people were packed so close together they could barely move . . ."

Voznesensky has felt such adulation often. In the Soviet Union today there is no movie star, no athlete, no ballet dancer better known than he is. Russia is a land that makes heroes out of those who write verses - and Andrei Vozsensenky, who is currently in Washington as a fellow at the Woodrow Wilson Center's Kennan Institute for Advanced Soviet Studies, is one of the most famous Russian poets in history.

His languid face with a mouth that pouts easily and eyes that go from sorrow to humor to icy cynicism in seconds is nearly as familiar to the many millions of Russians who have seen it for years on posters, in books and on television as the faces of their families.

Voznesensky's poetry would assure him stature almost anywhere. But to Soviets he is much more than just a fine stylist. Voznesensky is an artisto an accomplished showman and yet also a curiously elusive figure who upsets many Communist Party apparatchiks but still manages to stay inside the bounds of ideological propriety.

So that Americans might find out more about this complex man - and so that he might indulge a longstanding fascination with the United States - Fred Starr, secretary of the Kennan Institute, arranged for Voznesensky to make a three-month visit.

Every morning for the past couple of weeks Voznesensky has strolled from his furnished efficiency in a Southwest highrise to an office in the Smithsonian's castle building where the institute is located and worked there for several hours on the relationship of such great Russia 20th-century poets as Osip Mandelstam and Boris Pasternak to modern U.S. classics like T. SL. Eliot and Ezra Pount.

"So mich is different in the experience of their lives," Voznesensky said the other night, sipping from a small tumbler of vodka neat, "but so much is the same in the expression of the soul."

When the project is completed, Voznesensky is expected to produce some sort of research paper comparing later-day Soviet and American poetry. "I have already found an amusing symmetry," he said, "between a Russian futurist named Kamenski and your ownee, Cummings, (whose name in Russia is pronounced Kamensk."

Scholarship, however, is onlay a peripheral part of Voznesensky's pleasure at being here.

This will be the most extensive of five trips he has made to the U.S. over a period of 16 years. He has many good American friends - Teddy Kennedy, Arthur Miller ("I consider his farm sort of like a home to me here"). Stanley Kunitz and until his death last month, poet Robert Lowell.

The United States has long played a part in some of Voznesensky's most provocative poems. In February 1970, for instance, authorities in Moscow shut down a stage review in which Voznesensky equated the suicide of young poet Sergei Yesenin in 1925 with the assassination of Robert Kennedy, portraying both as victims of mankind's common cruelty.

Most recently, Voznesesnky has written a moving tribute to Lowell. The two had last met in Moscow in June and a comraderie that originated in the Russian's earlier visits to the U.S. took on a special intensity.

"He seemed older somehow, melancholy," Voznesensky recalled. "There was a good deal of drinking. I took him to see the grave of Pasternak at Peredelkino, a place of very great peace."

So it was that Voznesensky in his first days here of jet lag and general confusion rushed to the village of Dunbarton, N.H., where Lowell is buried. Later he wrote a poem about the visit . . .

How is it Robert, there in your wild land?

Within us we all bear our family graves

How can we name the heart of sorrow's flower

As it races past us through dark cosmic waves?

Here on the stone the name that you once had rests like discarded clothes

So through the labyrinth you've made you way?

Next week Voznesensky sets off on a tour around the country (he has an established New York booking agent visiting New York, California, Michigan, Illinois. There is a certain pecuniary benefit to his travels because Voznesensky gets to keep part of the proceeds. The bulk goes to the Soviet government.

Perhaps this time, he says, he'll find out what makes America tick: "I've stopped being a sightseer. I've been to the Empire State Building. I want to know more now." He has made the effort before. A poem called "Striptease" written some years ago ends this way:

"Are you America?" I'll ask like an idiot;

She'll sit down, tap her cigarette,

"Are you kidding, kiddo?" she'll answer me.

"Better make mine a double martini."

Voznesensky is 44 but looks younger which makes it easy to forget that it is almost 20 years now since he and Yevgeny Yevtushenko emerged as heirs to the Russian tradition of young poet-heroes. They surfaced in the period of the post-Stalin thaw in Soviet life, a time when Alexander Solzhenitsyn's "One Day in the Life of Alexander Denisovich" could be published, when previously taboo themes were being addressed.

The substained popularity of Vozhesensky - it has mellowed a bit from its initial near-frenzy - is hard for Americans to imagine. Wherever he goes there are rapturous fans - on a very cold night in Moscow last fall about 12,000 people showed up to hear him and Yevtushenko read in a stadium. Every new book is published in lots of 100,000 and sells out instantly, which usually means it is gone in a matter of hours.

Unravelling the genius of Voznesensky is complex. He is certainly a very good poet and at his best, specialists say, even a great one. He writes the sort of poetry Russians love of its romantic imagery, the imtimacy of secrets fathomed from intricate messages in the words.

Yet as a personality he is much cooler than Yevtushenko, less flamboyant, more calculating. Between the two, Yevtushenko is a shade more celebrated but Voznesensky is taken more seriously as a poet.

Voznesensky is superb as a reader. Dressed usually in black with very tight pants, he steps to the center stage, places his hands on his hips and declames with rhythmic cadences that range from the style of a torch singer to eloquent reserve. Performing is an important element in Russian poetry and Voznesensky does it better than almost anybody else.

Some Russians who have known Voznesensky for years find it hard to reconcile the detachment of his manner in private, and his guarded emotions with the passions of his poems and public appearances. Recognizing this puzzle in himself Voznesensky once explained:

"The poet is two people. One is an insignificant person, leading the most insignificant of lives. But behind him like an echo is the other person who writes poetry. Sometimes the two coexist, sometimes they collide; this is why certain poets have had tragic ends.Often the real man has no idea what path or what action the other will take. That other man is the prophet who is in every poem . . .

"When I read my poetry to a great number of people, their emotional, almost sensual expression of feeling seems to me to reveal the soul of man - now no longer hidden behind closed shutters, but wide open like a woman who has just been kissed."

In choice of theme and subject, Voznesensky is somewhat bolder in his approach to sensitive matters than most other leading Russian poets. He was often accused in the '60s of being a formalist - someone who is not sufficiently reverential to Socialist-Realist content.

When Nikita Khrushchev, the Soviet leader of the day criticized him harshly in 1963. Voznesensky responded gingerly but with hints of irony:

"It has been said . . . that I must never forget the sterm and severe words of Nikita Sergeivich (Khrushchev). I shall never forget them. I shall not forget not only these severe words but also the advice which Nikita Sergeivich gave me. He said: 'Work.' I do not justify myself now. I simply wish to say that for me the main thing is to work, work, work.

"What my attitude is to my country, to communism, what I myself am, this work will show."

In 1967 he was ordered to cancel a trip to the United States on political grounds. After he complained in a letter published in the French newspaper Le Monde, authorities refused to issue any of his books for three years.

Several of the poems Voznesensky reads to audiences here are controversial at home. "Nostalgia for the President," to take one of the best, has a subtle double meaning in Russia that turns it into an appeal for truth and honesty in public life.

A comic verse about the endless lines Russians have to wait on to buy anything was read in the stadium recital last fall but snipped out when the program was shown to the hinterlands on Soviet television. Such are the frustrations to Russian literary life.

For all that Voznesensky leads a very privileged existence by Soviet standards. He and his wife, Zoya, a talented prose writer, have a spacious apartment in a downtown luxury building that Joseph Stalin put up for hero workers (Yevtushenko has an apartment there also.)

The Voznesenskys have a lovely dacha set in the woods of Peredelkino about 30 minutes away, a short walk from the house where Pasternak lived. They entertain casually there, a few friends, good food, a little caviar. They wear elegant imported clothes and travel abroad as often as the party bureaucrats will let them.

On the night of his big stadium reading last year Voznesensky arrived late because his flight from Rome was delayed. And Zoya wanted to be there, but couldn't because she was getting ready to leave for Paris.

To earn all these perquisites Voznesensky fulfills his annual quota of provincial trips and factory visits grueling train and plane forays to places like Omsk and Tomsk in Siberia. He has never been publicly identified with dissidents such as Solzhenitsyn and steers clear of politics on his travels abroad. He is always grappling with censors behind desks and in his head.

What apparently has made it possible for Andrei Voznesensky to carry on for nearly two decades - whereas so many other Russian writers of skill have given up or gone into exile - is his sense of how to balance the integrity of his work with the pressure for political orthodoxy in a Communist state.

On this trip the most striking thing about the United States to Voznesensky is how bland it seems compared to previous visits. "Where are the new Andy Warhols, the Pop Art, the underground films, take Jesus Christ Superstars?" he asked. "You are in a duller period culturally, more neutral."

With the expectation of staying three months, Voznesensky is looking at the United States with more the eve of a new resident than a sightseer. "Is it safe to go for walks in Rock Creek Park in the evening?" he queried a friend. "I had to wait a week for a telephone to be installed in my apartment," he observed with some disapproval.

But there is no doubt either that Voznesensky is still very much of an exotic figure to Americans. On the way into New York City from the airport last weekend Voznesensky left a carrying bag in a taxi containing about $1,000 and some papers. About 2 a.m. the driver called the apartment Voznesensky was visiting after clearly trying all the others in the building.

"Is there a famous Russian poet there?" the driver asked.

It was arranged for the bag to be returned on Monday at the Chelsea Hotel where Voznesensky would be staying. Someone at the hotel tipped off the press so by the time the cab driver arrived there were crowds of reporters and television cameras to record the Soviet-America exchange.

In what might be described as poetry of a free-form sort, Voznesensky declared in English;

I lost my bag but I found something at the same time

I found that New York is not such a rough wild city as everyone had said

I lost my bag and found a good man

And maybe that is more important.

He offered the driver a $100 reward but it was politely declined.