On the basis of the nonlinear theory of membrane shells, a general finite-element procedure is developed for calculating the deformations in the stamping of sheet metal by arbitrarily shaped punches and dies. The sheet material is assumed to be elastic-plastic and satisfy a rate-insensitive, Mises-type flow rule taking into account finite deformation, work-hardening and normal anisotropy. Coulomb friction is assumed at the contacting surfaces between sheet and punch and between sheet and die. Numerical results obtained from application of the procedure to the hemispherical punch stretching of circular sheets are compared with existing axisymmetric solutions and experimental data.