Аннотация:The choice of construction materials preferred by modern industry more often are in the area of inhomogeneous ones. These materials have a complex internal structure, which lets them to be more effective in special problems required for new constructions, but on the other side, this internal heterogeneity makes them to exhibit complex mechanical properties. This work is dedicated to the analysis of nonlinear elastic response which is different in dependence on loading conditions. Several approaches to model elastic nonlinearity are analysed, and one, which can realize different stiffness for particular loadings and shear nonlinearity is demonstrated. Experimental correlation for proposed model is performed. By means of one of the proposed model, taking into account shear nonlinearity, combination with damage parameter is analysed. Composite specimen with the presence of concentrator was modelled and compared with experimental data.