Marc Blitzstein's "The Cradle Will Rock" has an almost legendary status in the annals of American musical theater -- not so much for its musical or theatrical quality (it is an interesting Depression-era period piece) but for its background story. That story is told brilliantly by director John Houseman tonight on PBS (10 p.m., Channel 26) as an introduction to the 1983 Acting Company of New York production, which may be definitive.

"Cradle" is an almost laboratory-pure example of propaganda set to music: the story of an effort to organize the workers in a place called "Steeltown, U.S.A." and the nefarious forces of capitalism, religion, the press, law enforcement, social pretension and artistic parasitism arrayed against them. Originally written under the auspices of the WPA's Federal Theater Project, it was found too controversial; the federal bureaucracy tried to suppress it and was aided by the Musicians' Union and the Actors' Guild.

The story of how the show limped to its triumphant opening night on June 17, 1937, is a rabble-rousing populist morality tale. In the final scene, locked out of the theater, the cast and audience trek 20 Manhattan blocks to another playhouse. The few hundred members of the original audience have invited their friends for a free show, and the crowd has grown spontaneously to a packed house, the way such things used to happen in Frank Capra's movies. Then Blitzstein, alone at the piano with no orchestra, scenery or costumes, begins to sing all the parts himself because the actors have been barred from performing it on the stage. Suddenly, a tentative voice is heard from one of the boxes; the performers have been forbidden to sing on stage but not offstage, and the members of the cast begin singing their parts from the audience. The show is, of course, a hit.

Houseman tells the story superbly; he was there in 1937, coproducing the show with Orson Welles, and his account has the well-worn polish of an oft-told tale. It nearly eclipses the show itself, but Houseman has directed this production with a fine sense of period style and of the material's potentials and limitations; his "Cradle" has exactly the right kind of rough polish and carefully controlled energy.

It needs this kind of help; the dialogue is frequently at the stylistic level of bumper stickers, and the characters have such resonant names as Mr. Mister (the steel mill owner), Reverend Salvation (who will preach anything if the price is right), Editor Daily (a tool of the special interests), Dr. Specialist (head of an antiunion committee), Harry Druggist (who sold out and then became an alcoholic) and Larry Foreman, a stalwart, square-jawed union organizer who laughs at death threats. The style is an almost perfect translation of Kurt Weill and Bertolt Brecht into American idioms -- like Blitzstein's definitive translation of the text of "The Threepenny Opera," which may be his most enduring theatrical work.

Outstanding in the large and generally fine cast are Patti LuPone, Brian Reddy, Mary Lou Rosato, David Schramm, Tom Robbins and Michele-Denise Woods.