It’s the early 20th century and a magnificent steam liner is about to depart England for New York. On the quayside stands Robert, the fifth officer welcoming arriving passengers. The first are three clerks traveling in second class, Dan, Henry and Stan, who tell Robert that one of them, Stan, is getting married and the other two would like to take him around brothels in New York. Robert says for a price he will set them up with lonely ladies on board the ship. Three lonely ladies, in fact, the wealthy Agatha Magness and her two nieces, Bertha and Beryl. Agatha is only interested in meeting rich, powerful people on board, but Bertha wouldn’t mind shacking up with one of these men ogling them. A dirty, grimy stoker then appears, scaring Agatha and forcing Robert to produce a whip to beat the poor man down below. Beryl is shocked by Robert’s behavior, especially since she sees something quite inviting about that stoker.
Scene two sees Bertha and Beryl on deck chairs next to their sleeping aunt, discussing the intimate business of men as Dan, Henry and Stan walk by, tipping their hats each time. Not knowing their names, the girls decide to give them numbers: 6, 12, and 22. Robert arrives to inform them that he is ready to give them all a tour of the ship. Being woken up suddenly, Agatha jumps to her feet and asks if the ship is sinking. Hardly, scoffs Robert, the ship is unsinkable. Agatha is none too happy about having to take the tour with the three gentlemen, lamenting that they are the only passengers out of the several thousand she has met so far.
A dark and steamy boiler room is the setting for scene three. Robert leads his party to a point where they can observe the stokers shoveling coal into the furnaces. Agatha is disturbed that the three gentlemen seem to show no interest in the ship. As she goes to find out why, Bertha tells Beryl that Robert will provide one or both of them with his cabin and one of the gentlemen for their pleasure. Beryl refuses, so Bertha offers herself up to Stan. Off they go despite Agatha’s protests that she hardly knows the man. Beryl assures her she will be all right, asking just to get the bloody tour over with.
The action next moves to the first-class dining room, where Agatha has invited the three gentlemen to join them as a way of saying thanks for handling her luggage on the pier. Before they arrive, Robert takes her to meet the mysterious Julian Westbrook, the grapefruit merchant who happens to be her neighbor on board and yet she has never even seen him. Bertha tells Beryl about her rendezvous with Stan and Beryl finally decides to go for it herself, also with 22. The gentlemen arrive in time to hear the girls joking about their numbers. Then Agatha comes, disgusted with the grapefruit merchant’s bragging, and reproaches the gentlemen for arriving late. Robert appears to inform the party that the captain has to remain on the bridge that evening because icebergs have been discovered in the area. He takes his place at the table, hardly what Agatha was expecting, but he more than makes up for it by listening to her boast about the exploits of her late husband. While she relates, Death enters and starts hovering around Stan, making him clearly uncomfortable. Suddenly he lets out a scream, forcing Dan to escort him topside. That leaves only 12 to go with Beryl, which is better than nothing, so off they go. When Robert goes to check on the dinner and Bertha heads for the ladies room, Agatha is left all alone at the table, wondering what other mishaps are in store for her on this voyage.
Bertha is alone in the girls’ cabin, having left her aunt at the table with Robert, when Beryl walks in and tells her that Henry flubbed their rendezvous. Never mind, she’s looking for real men and thinks she’s found him in the hairy, muscular stoker. Bertha can’t believe it, and is even more shocked to learn that the gentlemen paid Robert for the use of his cabin. Agatha walks in, taken by how charming a man Robert turned out to be, and secretively telling them that they are planning to meet on the bow the next day, where typically only young lovers and baboons hang out. After she goes off to bed, Bertha demands to know how much money they paid Robert.
Henry returns from his rendezvous with Beryl to find that Stan is plum crazy, on account of Death still annoying him. Dan is worried he has syphilis and that he might have caught it from Bertha, in which case Henry could be at risk if Beryl is also a carrier. Henry insists he has nothing to worry about, because Beryl was (is) a virgin. Robert knocks on the door and enters, causing Death to slip away. He’s there to ask the men if he could bunk with them for the night because he has given his cabin to another passenger. He dismisses the suggestion that Stan caught syphilis from Bertha and went crazy all in one day, especially when he can see that Stan, now that Death is on a break, seems to be all right and ready for more action.
Robert uses a walk on the bow to tell Agatha the story of his poor upbringing but how he nevertheless will someday rise up to become the captain of this ship. If only he weren’t so lonely. As if things weren’t bad enough, now Robert must escort Beryl down to the stoke hole to arrange a rendezvous for her with a stoker. He’s basically doing it out of extortion, because Beryl knows all about his pimping and gold-digging activities. He brings a stoker up, explains what’s required of him, and then waits around the corner with his whip. As the stoker removes his shirt, Beryl breaks out laughing, saying she never thought any man could be so hairy. She composes herself, but quickly breaks out laughing again at the sight of him. Only thanks to the intervention of Robert and his whip is Beryl saved from a frightful strangulation. But as they turn to leave, Robert notices that the stoker is shoveling more coal into the furnace than what the system can handle. With the boiler ready to explode, he beats the stoker senselessly, but to no avail. Finally he grabs Beryl by the hand and jumps as an explosion rips through the boiler room.
It’s topside, the deck is full of panic, and Agatha and Bertha are scrambling around calling out for Beryl. While Agatha goes to look for her below, Beryl shows up, explaining to Bertha what she did. At that moment Dan and Henry arrive and ask Robert, who they spy across the deck, for the key to his cabin so they can rescue Stan. When they leave, Bertha asks what the problem is and Robert tells her that they think Stan has syphilis. This causes her to faint, just as her aunt arrives and is relieved to see her niece. The ship’s bell sounds ordering people into the lifeboats, with Robert promising Agatha he’ll make sure she and her nieces have a place. The bell tolls again when the men arrive and Robert gives them the unfortunate news that only women and children are allowed in the lifeboats. Fine, say Dan and Henry, but at least he should take Stan. Robert refuses to let any lunatic on board and whips out a gun to drive home that fact as he disappears over the railing.
Safely in a lifeboat, Agatha demands to know of Robert why they left without the three gentlemen. When she refuses to be mollified with his excuses, he snaps at her to shut up. Finally understanding that he was only after her money, Agatha begins berating him, and he returns the favor by informing her that the ship is going down because one of her nieces wanted to have sex with a stoker. Now would she be so kind and sit down and let him be the hero of this saga? Hah, she scoffs, and declares a mutiny, whereby Robert whips out his pistol again and tells her he won’t warn her again. Agatha gives up any chance of taking over the life boat when it’s clear the other women won’t join her. But all is not lost. If she hands over her big, sparkling diamond, Robert will be happy to turn the boat around. She’s not happy about it, but complies.
The final scene opens with Dan and Henry using a shipboard axe in an attempt to make a raft. Henry is ready to use it on Robert when he reappears, backing off only at the sight of his gun. Agatha rushes on board, telling them she had to pay Robert to rescue them. Unfortunately they handcuffed Stan, still being haunted by Death, to the railing and don’t have the keys. The only way is to use the ax to cut through the chain, but Stan is squirming too much. Since Robert won’t help, Agatha will have to swing it while Dan and Henry try to hold Stan’s arm still. She can’t manage it, so she calls her nieces on board. Beryl doesn’t even try, but Bertha jumps right in there and swings away, chopping off Stan’s hand and creating more chaos on deck. When they refuse to give up on the poor creature, Robert shoots and Stan falls dead with Death on top of him. Agatha rushes at him with her fingernails, allowing Bertha to come in from behind and knock him unconscious with the ax. He falls on top of Death and the others make their escape in the lifeboat. Robert comes to, pleads with them to come back for him, then dismisses them, warning they’ll meet up again. He picks up the ax as a prelude to go looking for another lifeboat while Death slowly rises. As he leaves the stage, Death starts annoying him much in the same way she did Stan.