This diploma thesis focuses on realization of a computational model of fibre composite with elastomer matrix and on homogenization of properties of this composite. The work deals with computational modelling of strain-stress states which arise in mechanical tests of composites. The composites investigated by mechanical tests comprise of hyperelastic rubber matrix and steel reinforcing fibres. Computational modelling is carried out at two levels of the model. First, with three-dimensional modelling of fibres and matrix as two different materials and, second, using a homogenized model of composite; this constitutive model describes the composite as a homogeneous anisotropic material. It means that properties of fibres are encompassed into strain energy density by the mathematical formulation of the constitutive model. Further, the work deals with computational modelling of mechanical tests of hyperelastic isotropic materials used for identification of their material parameters and for verification of the selected constitutive model of material. For particular hyperelastic material, simulations of tests were carried out, namely of uniaxial tension, biaxial tension, uniaxial compression, biaxial compression, pure shear and uniaxial tension with constrained transversal strain (planar tension). Parameters of the constitutive model were determined of experimental input data. Verification of the constitutive model was carried out by comparison of the data acquired by experiments with the results of simulations of mechanical tests in FE program system Ansys. Then the authentic constitutive model of material was used for description of matrix behaviour in models of mechanical tests of composite material and results were compared with experimental data. Principal objectives which I want to attain are following: • to acquaint with the constitutive models of hyperelastic isotropic and anisotropic materials and identification of their perameters on base of mechanical tests. • to create computational models of testing specimens of composite “ rubber – steel fibre“ for different fibre arrangements and to use the created computational models in simulations of chosen tests. • to test the possibilities of computational modelling of composites with application of homogenized properties and to compare the results of both approaches. Results which were attained: • the computational models were created with the fibres modelled; the strain – stress characteristics are qualitatively corresponding to experiments, and quantitative difference is 20% - 40% (see (4.3)). • the computational models based on homogenization of properties were tested and gave results corresponding to the models with modelled fibres (see (4.4)) with a good accuracy.