AbstractThe return mapping algorithm is one of the most efficient procedures to solve elasto‐plastic problems. However, a criticism that may be lodged against this method is the difficulty of the practical computation of the consistent tangent matrix when the return is non‐radial. Much research has been done to handle this matrix. In this paper, a unified approach is presented in such a way that a simple closed‐form expression gives the consistent tangent matrix for the classical constitutive relations (von Mises, Tresca, Mohr–Coulomb, Drucker–Prager). The basic ideas are in the properties of eikonal equations appearing in several fields as image treatment, short time computation in elastic waves and others. The same kinds of ideas can be extended to non‐classical models. Copyright © 2003 John Wiley & Sons, Ltd.