The discovery of the wreckage of the RMS Titanic in 1985 attracted Yeston's interest in writing a musical about the famous disaster. "What drew me to the project was the positive aspects of what the ship represented – 1) humankind's striving after great artistic works and similar technological feats, despite the possibility of tragic failure, and 2) the dreams of the passengers on board: 3rd Class, to immigrate to America for a better life; 2nd Class, to live a leisured lifestyle in imitation of the upper classes; 1st Class, to maintain their privileged positions forever. The collision with the iceberg dashed all of these dreams simultaneously, and the subsequent transformation of character of the passengers and crew had, it seemed to me, the potential for great emotional and musical expression onstage."

Stone and Yeston knew that the idea was an unusual subject for a musical. "I think if you don't have that kind of daring damn-the-torpedos, you shouldn't be in this business. It's the safe sounding shows that often don't do well. You have to dare greatly, and I really want to stretch the bounds of the kind of expression in musical theater," Yeston explained. Yeston saw the story as unique to turn-of-the-century British culture, with its rigid social class system and its romanticization of progress through technology. "In order to depict that on the stage, because this is really a very English show, I knew I would have to have a color similar to the one found in the music of the great composers at that time, like Elgar or Vaughan Williams; this was for me an opportunity to bring in the musical theater an element of the symphonic tradition that I think we really haven't had before. That was very exciting."

The high cost of Titanic's set made it impossible for the show to have traditional out of town tryouts. Titanic's previews began at Broadway's Lunt-Fontanne Theatre in 1997 with major technical troubles: ironically, during previews the model ship onstage would not sink. These difficulties were mostly resolved by opening night, but the show received mostly negative reviews. The New Yorker's was a rare positive assessment from the New York press: "It seemed a foregone conclusion that the show would be a failure; a musical about history's most tragic maiden voyage, in which fifteen hundred people lost their lives, was obviously preposterous.... Astonishingly, Titanic manages to be grave and entertaining, somber and joyful; little by little you realize that you are in the presence of a genuine addition to American musical theatre."

Nevertheless, the show became a surprise hit. Many credit at least part of the show's success to former talk show host Rosie O'Donnell who championed the show, featuring members of the original cast on her daytime talk show and giving away tickets to members of her studio audience. The show got a further boost when it won the 1997 Tony Award for Best Musical among other awards. The release of James Cameron's film Titanic in December 1997 helped fuel worldwide interest in the disaster, and the Broadway production had attendance of 80% or more in the beginning of 1998, through August 1998, when attendance started falling.