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This work proposes approaches, which can be used for the description of the elastic properties of composite materials taking into account these types of nonlinearity. The proposed constitutive equations are based on special type of potential functions, which involves the dependency on parameters representing stress state type and the degree of shear deformation. Three different approaches are proposed. One of them is based on traxiality parameter only. In the second one, the special parameter is introduced, which characterizes shear deformation and can be used to model shear nonlinearity. The third approach is based on the use of both parameters, which are introduced in constitutive equations and has all the benefits from taking into consideration the stress state dependence of material properties, and nonlinear shear behavior.