Partial damage is considered in this paper. It is defined as a transformation of mechanical properties between two materials along a surface, in elasticity or plasticity. The transformation is controlled by a generalized energy criterion of the Griffith type. The equilibirum state of the structure, the total dissipation with increasing loading and the associated rate boundary value problem are studied within the frame work of standard materials. A global formulation of the rate boundary value problem allows us to charaterize the actual equilibrium state assumed to be known. Finally, the condition of stability and the possibility of bifurcation are given, as are applications to simple composite structure.