Brooke Shields in Israel's 'Sahara'

Can that be Brooke Shields behind the false mustache? And what on earth is Miss Shields doing at the wheel of a 1925 racing car speeding across the North African Sahara. . . er, in Israel?

The answer is that the teen-aged actress has begun the filming of ''Sahara.'' Budgeted at $15 million, the film is the largest production ever made in Israel.

It is a film inspired by the wrong-turn adventure last year of British Prime Minister Margaret Thatcher's son, Mark, who got lost during an auto rally in North Africa and by the box-office success of ''Raiders of the Lost Ark.''

Miss Shields plays the daughter of an American car developer who decides after her father's sudden death to race his latest creation in the first trans-Sahara auto rally in 1925. Since women in those benighted times were neither running governments nor competing in rallies, she pastes on a mustache and goes as a young man.

The film will be made almost entirely in Israel, masquerading without much difficulty as North Africa.

It will include a battle scene between warring ''Arab tribes'' staged by some 10,000 extras in the Negev Desert north of the Israeli resort town of Eilat. Most of the warring tribesmen, needless to say, will have names like Cohen, but producer Menahem Golan says many Israeli Arabs will also be in the cast.