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Composite materials play a significant role at present time for different structural industries. Many approaches to the stress analysis of structural elements made of this type of material exist and they are well developed. Nevertheless for the characterization of some effects that composite materials exhibit, still there are not exist standard and well working methods to take them into account during engineering simulation. This research work is dedicated to one of the set of the examples of noted effects, which are the nonlinear elastic material response to the action of external forces. It is very common for fiber reinforced materials to have different modulus in the dependence on the type of loadings; also it is usual for this type of materials to display nonlinear diagram in plane shear experiments. Common approach is based on the use of linear elastic material model with averaged properties. There are no generally accepted methods to model the noted effects, and the problem of developing of appropriate material model is still competitive one. This work proposes two possible approaches: the first one is for simulating of stiffness property dependence on type of loading and the second one is for taking into account nonlinearity of plane shear diagram. Also by means of second approach, the example of possible application is demonstrated on the base of the problem of a dry preform layup process.