Abstract Internal symmetry in the constitutive model of perfect elastoplasticity is investigated here. Using homogeneous coordinates, we convert the non-linear model to a linear system X ̇ = AX . In this way the inherent symmetry in the constitutive model of perfect elastoplasticity (in the on phase) is brought out. The underlying structure is found to be the cone of Minkowski spacetime M n+1 on which the proper orthochronous Lorentz group SO 0(n, 1) left acts. When the plasticity mechanism is shut off by the input path, the internal symmetry is switched to a translation group T( n) acting on the closed disc D n of Euclidean space E n . Based on the group properties a Cayley transformation is developed, which updates the stress points to be automatically on the yield surface at every time increment. These results (and their generalizations to more sophisticated models) are essential for computational plasticity. As an example, the results calculated using the group-preserving scheme and the exact constitutive solutions for a rectilinear path are compared.