Written in the form of an extended letter from Mrs. Basil E. Frankweiler to her lawyer Saxonberg, this novel details the adventures of Claudia and Jamie Kincaid.
Claudia is an intelligent twelve-year-old girl who loves nice things and is easily frustrated. She is particularly infuriated by what she perceives as ill treatment by her family, so she decides to run away to the Metropolitan Museum of Art in New York City (such a glamorous setting suits her). She decides to bring her brother Jamie, who has a great deal of money from carefully saving his allowance and beating his friend Bruce at cards.
After they find a 10-fare ticket with only 9 rides punched out, the children see their chance and take a train to New York City. They successfully hide in the Metropolitan Museum of Art for a week, hiding in toilet stalls while the guards make their rounds and blending in with school tour groups during the day. During the night, they sleep in historical beds that no guests are allowed to touch. They bathe in the museum fountain and live off snack food.
The children’s adventure collides with mystery when they encounter a new exhibit: the beautiful statue, Angel, which may have been carved by Michelangelo himself. They learn that Angel was purchased for an incredibly low price from the collection of a woman named Mrs. Basil E. Frankweiler.
The children conduct extensive research on the statue, and, one night, they discover the imprint of Michelangelo's artist's mark on a cloth where the statue previously stood. Excited, they anonymously present their findings to the museum.
However, a disappointing letter informs Claudia and Jamie that the museum has long been aware of this mark, which does not conclusively prove that Michelangelo created the statue. The children prepare to head home, but at the last minute Claudia impulsively purchases tickets to Mrs. Frankweiler's home in Connecticut.
Mrs. Frankweiler welcomes the children into her home, and offers them a deal: they have one hour to search her files for information on Angel. Thanks to Claudia's careful planning and Jamie's sudden inspiration, they discover a sketch of Angel by Michelangelo. The statue was indeed carved by him. Mrs. Frankweiler tells the children that they can have the sketch if they tell her the story of how they were able to hide out in New York for a week.
The children decide to adopt Mrs. Frankweiler as their grandmother, and head home having achieved their major goal: they feel truly different and special.