How does an invitation to a dancer arrive, asking her to become the first American artist ever to appear as a guest soloist with prestigious Soviet ballet companies? In a plain brown wrapper, naturally.

The artist is Eleanor D'Antuono, who was just recently in Washington dancing lead roles with American Ballet Theatre in such ballets as "Sleeping Beauty," "Les Sylphides" and "Theme and Variations." The 40-year-old dancer, a native of Cambridge, Mass., has been a principal artist of ABT for the past 16 years, and is widely esteemed for her versatility and prowess. She danced with the Ballet Russe de Monte Carlo as a teen-ager-the troupe's youngest member-in the '50s, alongside such notables as Alicia Alonso, Maria Tallchief, Igor Yous-Kevitch and Frederic Franklin.

During the ABT engagement at Kennedy Center, she took some time to talk about her recently completed and unprecedented Russian tour.

"I went down to pick up my mail one day," she said, "and there was this peculiar-looking brown envelope, stuffed very full. Inside was a large sheaf of papers, all in Russian. I didn't know Russian at all, but my girlfriend had studied some, so she dragged out her Russian dictionary and began plugging away. Suddenly she said, 'You know what this is? It's a contract. It's from Gosconcert, the Soviet cultural ministry, and they want you to go over there and dance for a month. There's a whole repertory here for you to select from, and you're supposed to sign on the dotted lin.'"

D'Antuono signed and returned the form, and went through the usual bureaucratic mill in this country to make application for such a trip. This was early last fall. For a long while, there was no further word, and she'd all but put it out of her mind.

Then she got a call from Swiss dancer Hans Meister, former director of the Zurich Ballet, who, it turned out, was to become her partner for the tour-he had danced a great deal in the Soviet Union, spoke Russian and knew the Russian ballet elite very well. "Haven't they told you yet?" he asked in astonishment. "Of course you're going. You open at the Kirov in 'Giselle.'"

The Kirov Theater in Leningrad, formerly the Maryinsky (under the czars) and home of the Kirov Ballet, is the central shrine of balletic art in Russia. Meister's call was the equivalent of telling a Soviet soprano that she was to open at the Metropolitan Opera in "Aida."

How did all this come about? Through a chain of circumstances stretching back some years, starting, perhaps, with D'Antuono's appearances in Russia with ABT on the company's tour in 1966. The favorable impression she made then had not faded in the interim.

Last year, the ballerina had appeared in a large international ballet festival in Cuba, at Alonso's invitation. Also there was Azari Plisetzki, brother of the Bolshoi's Maya Plisetskaya, who himself had been Alonso's partner with the Ballet Nacional de Cuba for a number of years. Afterward, Plisetzki told D'Antuono: "All Moscow has seen you now. I filmed everything you did in Cuba."

There were other connections. Celebrated dancer and pedagogue Natalia Dudinskyaya, who heads the Kirov's academy, had seen D'Antuono dance in London. Yuri Grigorovitch, artistic director of the Bolshoi Ballet, had already given her permission to perform the pas de deux from his ballet, "Spartacus," in the United States last year, making her the first American ballerina to do so. When she went to Paris to learn the choreography, she was referred to Hans Meister as a Russian-speaking dancer who could assist her. Later, in Leningrad, Meister proposed D'Antuono as a possible guest artist for the Kirov to that company's new director, Oleg Vinogradov.

D'Antuono did indeed open at the Kirov in "Giselle," to formidable acclaim, on a tour which took her as well to five Soviet cities including Riga, Vilnius and Kharkov, where she danced with the indigenous ballet troupes in such other works as "Swan Lake," and "Les Sylphides," as well as "Giselle."

She remembers well the triumphs, as well as the unstinting personal hospitality with which the Russians received her. "I literally never had a lunch or a dinner out," she said. "So many opened their homes to me-Dudinskaya treated me like a member of the family." But she also recalled the tribulations of an unforgettable experience.

"I left from Paris on New Year's Eve, and it was pelting rain," she said. "There I was in the boarding area with my six tutus and my 35 pairs of toe shoes, and there wasn't a soul around. I thought for sure I missed the flight. Finally an attendant came up and said, 'You're on the flight to Moscow, yes? You are our only passenger!' I had a whole Air France 707 to myself."

In Leningrad, she was royally domiciled, but there was a hitch. "They put me in the Astoria, it's beautiful hotel. I had a five-room corner suite with two baths and all 17th-century French antique furniture. But it was freezing. The winter was unusually severe-it was like 40 below in Leningrad-and there was something wrong with the heat. I slept that first night with thermal underwear, wool stockings, ski pants, my fur coat, fur hat, gloves and all the blankets from all the beds-and I was still cold. I woke up the next morning and it was impossible to change clothes or take a shower."

Her room was changed to a smaller but more bearable suite, but the temperature problems followed her into the Kirov dance studios, which she also found too chilly to tolerate. She ended up taking class with the men because their studio for some reason turned out to be "boiling warm."

Dudinskaya, her partner Meister and some of the Russian ballerinas helped accommodate D'Antuono to the different choreographic versions the Russians perform in the classic repertoire, as well as their distinctive style of movement. "A ballet like 'Swan Lake,'" D'Antuono observes, "is different from city to city. The music is different, the steps are different, in some cities a whole act may be different than the versions we know in the States. In Russia, for example, there's often a lot of dancing for Von Rothbart, the evil magician who's usually only asked to pantomime in the West. In one city, I had a long duet with Von Rothbart in the Black Swan section."

One thing she was to prepared for was the effect of the steeply raked stages in Russia. "I was told the stages would be raked, but it's a different thing when you experience it. Not only in the theaters, but in the studios. It was like having to learn how to stand up all over again.

"It was lovely for jumping, and I got used to that quickly. But it was murder on pirouettes and balances, and the trouble was, everywhere you went the stage was different. Some were flat, and some made you feel as if you were sliding down a hill."

In Vilnius, she found herself assigned an extraordinary personal factotum. "He appeared at my dressing room door-a tall, slim, very handsome gentleman with slickly combed hair, wearing tails and a red vest. He bowed to the ground and said, 'What can I bring you, madam? Hot tea or cool? Is there anything you need?' I was thrilled, but I kept having to stop myself from calling him Jeeves."

In Riga, she saw an evening of contemporary Soviet ballets. "They looked very tame and old-hat by Western standards," she said. "but they used electronic music and something they call rock, too."

Everywhere D'Antuono went she was plied with questions about the United States and its dance world, about which the Soviet public seemed to have little clear notion. One woman wanted to know if the ballerina wouldn't teach some classes in jazz dance. There was much interest in the Western ballet repertory. There were questions, too, about the celebrated Soviet dancers who had abandoned their mother country for the artistic freedom of the West. "They asked if we thought Baryshnikov was wonderful, and did I know Makarova. They asked about Nureyev too, but not as much, they seemed more used to his being gone by now. They were very curious about them, how Americans received them, how they lived, whether they were 'rich.' They seemed to take great pride in them still, basking in their American success." No one, however, asked a single question about Valery Panov, the Jewish, ex-Kriov star whose appeal for emigration led to official harassment and imprisonment.

Ballet is booming in the Soviet Union, as it is here, but for Russia that's nothing new. "In Russia," D'Antuono notes, "the ballet public is everybody. They are dying for tickets. They queue up in long lines-outside the theater-to wait for you after the performance to take a picture, to ask for an autograph, just to get a glimpse. Maybe not everyone goes to the ballet, but everyone knows about the ballet." CAPTION: Picture, Eleanor D'Antuono flew to Moscow with six tutus and 35 pairs of toe shoes: "I had an Air France 707 all to myself." By Martha Swope