On Floating Bodies (Greek: Περὶ τῶν ἐπιπλεόντων σωμάτων) is a work, originally in two books, by Archimedes, one of the most important mathematicians, physicists, and engineers of antiquity.

Archimedes lived in the Greek city-state of Syracuse, Sicily, where he was known as a mathematician and as a designer of machines, some of which might have helped keeping Roman armies at bay during the Second Punic War.

[2] Archimedes' interests in the conditions of stability for solid bodies are found both here and in his studies of the lever and centre of gravity in On the Equilibrium of Planes I-II.

Most notably, On Floating Bodies I contains the concept which became known as Archimedes' principle: Any body wholly or partially immersed in a fluid experiences an upward force (buoyancy) equal to the weight of the fluid displacedIn addition to the principle that bears his name, Archimedes discovered that a submerged object displaces a volume of water equal to the object's own volume (upon which the story of him shouting "Eureka" is based).

[4] Book two of On Floating Bodies is considered a mathematical achievement unmatched in antiquity and rarely equaled until after the late Renaissance.