An approach is offered for evaluation of effective stress-strain curves of particulate composites under plane strain conditions based on a solution of the boundary-value problem providing simultaneously the data on the corresponding structural stress and strain fields. The influence of randomness in the particle arrangements and the filler concentration on the effective behavior is established. It is demonstrated that the observed plateaus on the tensile and compressive curves are caused to a degree by the geometrical non-uniformity of the composite structures. The difference between tensile and compressive curves is examined and explained from the structural point of view.