Claudia Kincaid is tired of the injustice and mundaneness of her life. Being the oldest of four kids, she is responsible for more chores and gets less allowance than anybody else in her class at school. She chooses her brother Jamie to join her, mostly because he has a lot of money, and plans almost every detail of how they’ll run away to the Metropolitan Museum of Art in New York City.
Claudia and Jamie pack their instrument cases with clothes and duck down in the back row of the school bus, then boarding a train unnoticed. Claudia mails a note home letting her parents know not to call the FBI. Arguing time and again about decisions on where to go and what to spend money on, the two Kincaids make it to the museum and scope out a place to sleep for the night.
After a successful night of sleeping in the museum, Claudia and Jamie hide out in the bathroom until the museum is open to the public.They eat breakfast and decide to visit a new exhibit each day, beginning with the Italian Renaissance. It is especially crowded in this section of the museum; a beautiful new angel statue is on display with news reporters snapping photographs. The next day, Claudia and Jamie find a discarded newspaper and read about the statue; it is believed to be the work of Michelangelo and was purchased for only $225.00 from Mrs. Basil E. Frankweiler. (Claudia misses the section of the newspaper that describes their disappearance.) Claudia and Jamie are eager to find out the truth about the statue.
Claudia and Jamie spend hours at the library reading and looking at photographs to gather information about the statue. Back at the museum, they find a clue about the Angel; there are initials carved into the bottom of the statue. They write an anonymous letter to the museum and purchase a P.O. Box to wait for the response. After a few days, they receive a letter informing them that the museum is aware of the clue and experts are still searching for more information before they can make any determination. Claudia is very disappointed and feels like a failure. Jamie suggests returning home, but Claudia cannot stand the idea of returning home the same person; she wants to be different in some way.
Claudia and Jamie get the idea to visit Basil E. Frankweiler to get information. They use the rest of their money to take a taxi to her home in Farmington, Connecticut. At first, Mrs. Basil E. Frankweiler refuses to see the children, but after Jamie announces who they are, they are escorted to her office. During this visit, Mrs. Frankweiler gets to know the children and decides to bargain with them: she will share her secret of the Angel if they tell her all the details about running away. Claudia and Jamie look through the files in Mrs. Frankweiler’s office and find a sketch which is proof that Angel was created by Michelangelo. Claudia is happy to know this secret, and is surprised when Mrs. Frankweiler says that she will leave the sketch to Claudia and Jamie in her will.
Claudia and Jamie are escorted home the next evening by a chauffeur. Mrs. Basil E. Frankweiler reveals to readers a secret that she kept from the children: the lawyer who she is writing to is also Claudia and Jamie’s worried grandfather.