The prologue is a letter from Mrs. Basil E. Frankweiler, "To my lawyer, Saxonberg", accompanied by a drawing of her writing at her office desk. It is the cover letter for the 158-page narrative, which provides background for changes to her last will and testament.
Twelve-year-old Claudia Kincaid decides to run away from home happily, because she thinks her parents do not appreciate her and she doesn't like it. She chooses the Metropolitan Museum of Art (the Met) in New York City, with nine-year-old brother Jamie as companion partly because he has saved all his money. With one unused adult fare that she found in a wastebasket, Claudia found a way to get there for free on the commuter train and one very long walk.
Early chapters show how Claudia and Jamie settle in at the Met: hiding in the bathroom at closing time from staff on circuit to see that all the patrons have departed; blending with school groups on tour, to learn more about the museum exhibits; bathing in the fountain, whose "wishing coins" provide income; sleeping in an antique bed.
A new exhibit draws sensational crowds and fascinates the children: the marble statue of an angel, sculptor unknown but suspected to be Michelangelo. It was purchased at auction from Mrs. Basil E. Frankweiler, a collector who recently closed her showcase Manhattan residence. They research it on site and at the Donnell Library, and give their conclusion to the museum staff anonymously.
After learning they have been naive, the children spend the last of their money on travel to Mrs. Basil E. Frankweiler's home in Connecticut. She recognizes them as runaways but sets them briefly to the task of researching the angel in her long bank of file cabinets. Despite the idiosyncratic organization of her files, they do discover the angel's secret. In exchange for a full account of their adventure, she will leave the crucial file to them in her will, and send them home in her Rolls-Royce. It's a deal.
Claudia learns her deep motive for persisting in the crazy search: she wanted a secret of her own to treasure and keep. Mrs. Frankweiler may get "grandchildren" who delight her. Her lawyer gets a luncheon date at the Met, to revise her will.