The mechanical properties of a material describe the relations between the stresses acting on the material and its resulting deformations. Stresses capable of producing permanent deformations, which remain after the stresses are removed, are considered in this chapter. The effects of cryogenic temperatures on the mechanical properties of metals and alloys are reviewed in this chapter; the effects on polymers and glasses are discussed briefly. The fundamental mechanisms controlling temperature-dependent mechanical behavior, phenomena encountered in low-temperature testing, and the mechanical properties of some representative engineering metals and alloys are described. Modifications of test procedures for low temperatures and sources of data are also included.