You cheered for her in "National Velvet," she shocked you in "Who's Afraid of Virginia Woolf?," you swooned at her love scene in "A Place in the Sun," and you wept for her in "Jane Eyre." Now, for the first time, you will be able to applaud Elizabeth Taylor in the flesh, beginning next March 18 at the Eisenhower Theater.

Taylor will make her stage debut as Regina in a new production of Lillian Hellman's "The Little Foxes." No director or supporting cast has yet been chosen for the play, which was selected only this week after Taylor read through several other plays, including "Who's Afraid of Virginia Woolf" and Noel Coward's "Hay Fever."

Casting for the show will begin on Monday, Dec. 1, producer Zev Bufman said rehearsals cannot begin until Jan. 27 because Taylor, as the wife of a prominent Republican senator, John Warner of Virginia, will be taking an active part in the Reagan inaugural ceremonies. After one month of rehearsals, the show will open at the Parker Playhouse in Fort Lauderdale, Fla., on Feb. 27. From the Kennedy Center, it will go to New York, opening at a still-unnamed theater on April 30 after a week of previews. Although she has been a fixture on the motion-picture scene since "Lassie Come Home" in 1943, Taylor has never apeared on Broadway.

Bufman, who is also the producer or co-producer of the recent revivals of "Brigadoon," "Peter Pan," "Oklahoma!" and "West Side Story," said the idea for the new production originated at the opening night of "Brigadoon" at the National Theater in Washington. "Elizabeth came to the opening with Mrs. (Jouett) Shouse," he said, "and that's the night we met. We started talking about the theater, and she loved 'Brigadoon' so much that afterwards she came backstage to the cast party. I asked her, 'Why don't you do a play?' and under the influence of the evening, the excitement, meeting and talking with the cast, she agreed. I don't think I could have persuaded her so easily had she not experienced this rather tense and happy evening. She was infected with the theater bug, and that did more than any amount of conversation or negotiations through managers could have done."

Taylor could not be reached directly for comment, but she offered a statement through a spokesman: "I've always wanted to do a play on Broadway and finally, with my husband's support, I have the time, the opportunity and the enthusiasm to do it next year."

The choice between "The Little Foxes" and "Hay Fever" were so close, Bufman said, that "We were saying, 'Why don't we do them both in repertory?' But we were kidding, of course; that would be impractical. I think this will be the beginning of a major new stage career -- but her next show will have to be an original."

To settle details of Taylor's stage debut, an audition was held in New York not for actors but for scripts, Bufman said. "We asked some very good actors in New York to come to Mrs. Warner's suite and over coffee and soft drinks, peanuts and pretzels, we read through the plays -- an actor for every role -- around the coffee table. In a sense, it was really her audition, because none of the other actors were up for any parts. We had about 20 very high-caliber people, all of whom were working already and not there with the ulterior motive of getting a job -- people like Derek Jacoby, who has received such good notices in 'Suicide' and 'Hamlet.'

"'The Little Foxes'emerged as the most convincing piece, although Noel Coward's 'Hay Fever' was quite a terrific temptation; it's a wonderful high-style comedy and most people would be expecting Elizabeth to do a hard hitting dramatic piece. We read it the day before yesterday [Tuesday], but then when we read 'The Little Foxes,' it was so powerful there was no further question. She brings a special vulnerability to a role that is usually played icy-cold and vengeful. We're in for a multi-leveled performance, where years of film experience will be brought into a new theatrical experience. I think we will see a major new Broadway star emerging from the American film tradition."