Impregnating polymeric matrix with stiff particles may significantly improve structural response of a composite material. Such improvements have to be weighed against the effects of the stress concentration at the particle-matrix interface that influence local strength and toughness. in the present paper we elaborate on the issue of local stresses and strength in particulate polymer matrix composites considering polyurethane matrix impregnated with alumina particles in numerical examples. The parametric analysis presented in the paper is concerned with the effects of the particle volume fraction and the particle-to-matrix stiffness ratio on the local stresses and initial damage. We also discuss the resilience of the impregnated polyurethane, i.e. the density of energy necessary to produce initial damage. The approach to the analysis of fracture in the composite with initial damage is discussed accounting for available experimental observations. Three scales of fracture corresponding to different phases of the development and propagation of the crack are identified, including microfracture at the particle-matrix interface and mesofracture limited to the matrix surrounding the particle. While these scales of fracture should be analyzed by numerical methods, macrofracture that occurs after the crack “emerged” from the representative unit cell where it originated can be considered using available analytical techniques. The methodology of the stress analysis of a particulate material consisting of an incompressible hyperelastic matrix and much stiffer elastic particles is also proposed in the paper.