Titanic's designer, Thomas Andrews marvels at the wondrous things mankind has accomplished ("In Every Age"); with the R.M.S. Titanic becoming the newest feat once thought impossible. Stoker Fred Barrett arrives at the dock in Southampton, amazed by the feat of engineering ("How Did They Build Titanic?"). He is joined by Lookout Frederick Fleet and wireless telegraph operator Harold Bride, and they gaze in awe at the "Ship of Dreams" ("There She Is") as the crew arrives. J. Bruce Ismay, Andrews, and Captain E. J. Smith congratulate each other on being the owner, designer, and captain of "The Largest Moving Object" in the world. The ship's passengers arrive; the Third and Second Class passengers feel privileged to be aboard the maiden voyage of the grandest ship ever to sail ("I Must Get on that Ship"). The First Class passengers arrive; their names and achievements are narrated by Second Class passenger Alice Beane ("First Class Roster"). The Titanic sets sail, and the assembled company wishes her a safe crossing ("Godspeed Titanic").
Now at sea, Ismay arrives on the bridge to inform Smith that he plans for the Titanic to arrive in New York on Tuesday afternoon rather than Wednesday morning, while Andrews insists that the maiden voyage be a safe one. As they've cleared land, Smith allows her speed to be increased slightly. Barrett, in the boiler room, disagrees with the order on such a new ship, but nonetheless complies ("Barrett's Song").
As the voyage continues, Ismay demands increasingly more speed, so the ship can build an impressive reputation. Smith complies despite Andrews' objections and warnings of icebergs in their course. Smith hails 1st Officer Murdoch's qualities, deeming him ready to assume a command of his own, but Murdoch feels he is not yet ready to handle the responsibilities of the job ("To Be a Captain").
In Second Class, Alice Beane longs for the grandeur that is First Class, while her husband Edgar, a successful hardware store owner, is content with their station. Charles Clarke, who is traveling to America to become a journalist, is accompanied by his fiancee Caroline Neville. Caroline's father doesn't approve of the engagement, so they are eloping to America. In First Class, the titans of industry recount the accomplishments that man has recently achieved, with the Titanic becoming the pinnacle. ("What a Remarkable Age This Is!"). In steerage, three Irish lasses—each named Kate—dream with the rest of Third Class of the opportunities that await them in America ("Lady's Maid"). Kate McGowan is smitten with a young man traveling with them, Jim Farrell.
In the wireless room, Bride is overwhelmed by the passengers' personal messages to be sent, though he finds time to handle Barrett's proposal to his girlfriend ("The Proposal/The Night Was Alive").
On Sunday morning, the First Class attends religious services ("God Lift Me Up"), then dances on deck to "The Latest Rag". Alice Beane has managed to infiltrate their ranks, though she is turned away several times by an alert steward. Edgar finds her and the two argue over their lifestyle choices ("I Have Danced"). As evening draws near, the temperature drops, and lookout Fleet finds the weather conditions difficult for spotting icebergs ("No Moon"). On deck, Kate McGowan tells Farrell that she needs to marry as she is carrying the child of a married man, and he accepts. Elderly passengers Isidor and Ida Straus discuss their plans for the years to come while Charlotte Drake Cardoza scandalizes the First Class men by joining them for cards in the First Class Smoke Room ("Autumn").
Suddenly, Fleet spots an iceberg and alerts the bridge. Murdoch, who's the senior officer on the bridge, takes evasive action, but the Titanic strikes the iceberg.
The stewards begin waking the confused passengers, while they themselves do not have much information ("Wake Up, Wake Up"). Capt. Smith arrives on the bridge and is briefed on the situation. He orders all passengers to put on life vests, for Bride to begin sending distress messages, and for Andrews to inspect the damage. Andrews informs Smith and Ismay that the damage inflicted is more than the ship is designed to endure and that the ship will sink, reminding them that there are only enough lifeboats for less than half of the people aboard.
In the First Class Dining Salon, passengers refuse to believe that anything is wrong with the ship and are annoyed at being awakened in the middle of the night ("Dressed in Your Pyjamas in the Grand Salon"). Crew members are assuring them that there is no reason to panic. No one is aware of the ship's growing peril until a food cart rolls on its own, showing the ship's growing tilt. All the passengers and crew members quickly hurry to the lifeboats.
In Third Class, the three Kates and Farrell attempt to find a way up to boat deck, but are unable to until they are assisted by Barrett ("The Staircase"). Smith arrives in the radio room where Bride informs him that only the Carpathia is near enough to help, but is unable to arrive until after the Titanic has sunk. Smith, Andrews, and Ismay argue over responsibility for the disaster ("The Blame").
Women and children are ordered into the lifeboats, while the men are forced to stay behind ("To the Lifeboats"). Murdoch orders Fleet and Barrett into the last lifeboat to help man the oars, but Barrett doesn't know how to row a boat and lets Farrell, who can row, into the boat instead. Barrett bids farewell to his absent girlfriend while the rest of the passengers do the same to their loved ones ("We'll Meet Tomorrow").
The bellboy tells the captain that all the life boats have been launched, and that those remaining aboard accept their fate. Murdoch tells the Captain that he takes full responsibility for the accident, but Smith forgives him and then laments on how he had gone his entire career without experiencing any accident. Henry Etches, the first class steward, says a prayer ("To Be A Captain" (Reprise)). Isidor and Ida Straus (Ida had refused to leave her husband behind) affirm their long-lasting love for one another ("Still"). As the Captain declares the ship officially lost, Andrews—life vest unworn—remains in the first-class smoking room, obsessing over the ship's plans. He visualizes redesigning her as well as the final moments of the souls left aboard as the ship sinks beneath the waves ("Mr. Andrews' Vision").
In the early hours of the morning, the survivors are rescued by the Carpathia. Many of them recount the tragedy of the Titanic, mourning the loss of people and ship. Bride and Ismay, along with several of the survivors, discuss the possibilities that could have prevented the disaster ("The Foundering"). The survivors express hope that they will one day be reunited with their lost loved ones and abandoned dreams ("In Every Age/Finale").