Jo Armitage (Anne Bancroft) seems to be losing it while her husband Jake (Peter Finch) is unable or unwilling to help. In flashbacks, Jake is shown to be her third husband after having several children. She continues to have children with Jake. Jake sends Jo to a psychiatrist. He suggests that Jo wants to sanctifies sex by reproducing. While Jake is a good provider, she suspects him of improprieties. After getting pregnant, the psychiatrist and Jake suggest getting an abortion and sterilization. After the operation, things are going great and then Bob Conway (James Mason) brings evidence that Jake is cheating with his wife.
The title refers to the nursery rhyme Peter Peter Pumpkin Eater. Jo is a perplexing character. She is struggling but she is not crazy. It is an interesting character but I am of two minds about it. It allows Bancroft to do some good acting but it is also hard to fully invest in her. There is an attempt at surrealism with the cigarette smoke going backwards. Maybe more of that surrealism would allow the audience to feel her troubled mind.