<p>A model was developed to describe the behavior of ‘matrix–inclusion’ powder composites, whose properties are sensitive to loading and deformation patterns, particularly under tension and compression. Stress–strain relationships were proposed with a new material parameter m, which characterizes the tendency of materials to exhibit different resistance in tension and compression. Building on the research findings of Kachanov et al., the physical meaning of this new parameter within modified elasticity theory was established, and its connection with structural defects in the composite was identified. The relationships between the effective elastic characteristics of the composites and the content of defects of various types arising from the powder-based origin of the material were analyzed, with particular consideration of inclusions and the degree of their bonding to the matrix. Primary attention was paid to materials where the defects were volumetric pores and two-dimensional cracks. The results were further used to study elastic wave propagation within the modified model of a powder composite with differential resistance. In general, contrastingly to classical elasticity theory, the propagation velocities of longitudinal and transverse waves in powder composites were not material constants but depended on the dynamic loading pattern, which can be described through the ratio of bulk to shear strains. The dependence of wave velocity on loading pattern may serve as a basis for assessing the degree of imperfection in materials, while the established relationship between the degree of differential resistance and the content of various defect types can be applied to evaluate the contribution of each defect to the service properties of the material.</p>