An analytical framework which incorporates damage propagation/growth into the general structural stability analysis is presented. Therefore, the conventional total potential energy approach is extended by introducing an extended total potential energy-like functional capable of describing inelastic processes in which equilibrium holds between available and the required force for producing a change in structure. The work deals with systems which are described by I generalized coordinates and K damage parameters. The damage parameters are found to be functions of I generalized coordinates and M load parameters. The underlying variational principle for inelastic solids may be solved using discrete formulations or approximate methods such as a Rayleigh–Ritz formulation. This leads to a set of non-linear algebraic equations, comprising post-critical equilibrium paths and damage propagation. In order to verify the framework, it is applied to the well-known problem in which a delaminated composite strut/plate is subjected to an in-plane compressive load.