Continuum mechanics is a branch of physics that deals with solids and fluids (i.e., liquids and gases). Continuum mechanics makes the assumption that these materials are continuous: the fact that matter is made of atoms is ignored. Therefore, physical quantities, such as space, time, energy, and momentum can be handled in the infinitesimal limit. Differential equations are thus the mathematical tool of choice for continuum mechanics. These differential equations are often derived from fundamental physical laws, such as conservation of mass or conservation of momentum.

The physical laws of solids and fluids should not depend on the coordinate system of the differential equations. Continuum mechanics thus uses tensors, which are mathematical objects that are independent of coordinate system. These tensors can be expressed in coordinate systems, for computational convenience. See tensor analysis for more information.

There are two main branches of continuum mechanics:

The boundary between these two branches is blurry, because elasticity handles materials with viscosity.

See also: equation of state