The problem of stability of a quasi-static evolution of a solid is discussed in the framework of standard plasticity and visco-plasticity. General results concerning the criterion of second variation of energy are presented. Two different approaches are considered to discuss this problem for visco-elastic, visco-plastic or elastic-plastic solids. The first approach is based upon the linearization method and gives the asymptotic stability of the evolution of a visco-elastic solid when the associated dissipation potential is quadratic and positive-definite. The second approach introduces a direct analysis of the evolution in a nonsmooth but convex framework of plasticity and visco-plasticity.