The prologue is a letter from Mrs. Basil E. Frankweiler, addressed "To my lawyer, Saxonberg", accompanied by a drawing of her writing at her office desk. It serves as the cover letter for the 162-page narrative, and provides background for changes to her last will and testament.
Twelve-year-old Claudia Kincaid decides to run away from her home in Greenwich, Connecticut because she thinks that her parents do not appreciate her. She takes refuge in the Metropolitan Museum of Art (the Met) in New York City with her brother Jamie. She chooses Jamie as her companion partly because he has saved all his money. With the help of an unused adult train fare card that she found in a wastebasket, Claudia finds a way to get to the museum for free using the commuter train and a very long walk.
Early chapters depict Claudia and Jamie settling in at the Met: hiding in the restroom at closing time, as security staff check to see that all the patrons have departed; blending in with school groups on tour; bathing in the fountain; using "wishing coins" for money; and sleeping in Irwin Untermyer's antique bed.
A new exhibit draws sensational crowds and fascinates the children: the marble statue of an angel, the sculptor unknown but suspected to be Michelangelo. It was purchased at auction, for only a few hundred dollars, from Mrs. Basil E. Frankweiler, a collector who recently closed her showcase Manhattan residence. The children research it on site and at the Donnell Library, and give their conclusion to the museum staff anonymously.
After learning that they have been naïve, 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 from files in her long bank of cabinets. Despite the idiosyncratic organization of her files, they discover the angel's secret—Mrs. Frankweiler has purposefully "given away" a virtually priceless Michelangelo to the Met. 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.
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 (who is revealed to be the children's maternal grandfather) gets a luncheon date at the Met, to revise her will.
