This article presents formulas for calculating the following: effective stress, strain, and strain rate (isotropic material) in arbitrary coordinates and in principal coordinates; compression testing, tension testing, and torsion testing of isotropic material; and Barlat's anisotropic yield function Yld2000-2d for plane-stress deformation of sheet material. It also contains formulas related to flat (sheet) rolling, conical-die extrusion, wire drawing, bending, and deep drawing of cups from sheet metal.