The present paper describes a micromechanics-based approach to the strength properties of composite materials with a Drucker–Prager matrix in the situation of non-associated plasticity. The concept of limit stress states for such materials is first extended to the context of homogenization. It is shown that the macroscopic limit stress states can theoretically be obtained from the solution to a sequence of viscoplastic problems stated on the representative elementary volume. The strategy of resolution implements a non-linear homogenization technique based on the modified secant method. This procedure is applied to the determination of the macroscopic strength properties and plastic flow rule of materials reinforced by rigid inclusions, as well as for porous media. The role of the matrix dilatancy coefficient is in particular discussed in both cases. Finally, finite element solutions are derived for a porous medium and compared to the micromechanical predictions.