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This paper deals with the creation of computational models of a multilayer composite with long fibres and a polymer matrix in order to use them for shear test computational simulations. The research involves the determination of the material parameters of the matrix, in this case an elastomer is used as the matrix. Attention is given to the Mooney-Rivlin parameters obtained from tensile tests of the elastomer for the purpose of these simulations, because shear tests have not been performed. APDL in ANSYS was chosen to create the computational model. The outputs from the computational modelling will greatly help to refine the orthotropic parameters of the composite as a whole, which will be used in the computational simulations of the tyres.