A model is proposed for the deformation of elastic-plastic particle reinforced composite materials of a periodic structure with allowance for the damage. The model is based on a variant of the deformation theory of plasticity under active loading, in which the damage parameter is introduced, taking into account the difference in the accumulation of damage in phases during shear, tension and compression. The method of asymptotic homogenization of periodic structures was used to model the effective characteristics of elastic-plastic composites. Examples of numerical calculation are carried out for particle-reinforced metal composite - aluminum matrix filled with SiC particles.