Indestructible Object is the sixth EP by They Might Be Giants, released through Barsuk Records on April 6, 2004.

The EP's title comes from a famous work by Man Ray, also known as Object to Be Destroyed.

The tracks "Memo to Human Resources" and a different version of "Au Contraire" are featured on the band's tenth studio album, The Spine, which was released three months later.

The track "Ant" is a re-recording of a B-side from two of their 1990 singles ("Istanbul (Not Constantinople)" and "Birdhouse in Your Soul").

"Caroline, No" is a cover of the Beach Boys' song of the same name from their 1966 album Pet Sounds.