A formulation for the elasto-plastic constitutive matrices on discontinuities on yield surfaces is presented, for use in finite element calculations. The formulation entails no rounding of the yield surface or the plastic potential, as it is done in most other formulations, and therefore exact analytical solutions can be approached. Computational examples are given with the Mohr-Coulomb, the Modified Mohr-Coulomb and the Hoek-Brown models.