There are two main conflicts in the story. The first is between Mary Maloney and her husband. The second is between Mary Maloney and the police. At the beginning of the story, Mary's husband tells her that he is leaving her—or at least, Dahl implies as much. We don't actually hear her husband say that he is leaving her, but he does say that he will give her money and see that she is "taken care of." Not long after this, Mary hits her husband in the back of his head with a frozen leg of lamb, killing him instantly. This conflict between the husband and wife is the catalyst for the rest of the story.

Later in the story, the police call by Mary's house to investigate her husband's death. Mary pretends to the policemen that she is an innocent and distraught widow and that she is desperate for the police to catch the man responsible for murdering her husband. Mary even feeds to the policemen the cooked leg of lamb with which she killed her husband. Throughout this scene, there is a conflict or tension between Mary and the police. Mary tries to mislead them, and they try to discover the truth of her husband's death.

The conflict between Mary and the police is resolved when the police unwittingly eat the murder weapon. As soon as they begin to eat the lamb, we, the readers, know that Mary will avoid capture. Mary seems to know this too. Indeed, the story finishes with Mary laughing to herself in the other room while the police officers sit in the kitchen eating the lamb and wondering where the murder weapon might be.