We consider composites made of hydrogenated nitrile butadiene rubber (HNBR) and particles of zirconium tungstate (ZrW2O8). We focus on finite element (FE) modelling of a finite-strain mechanical behaviour of the composite and validation of the numerical simulation against experiments. Based on examination of composite microstructure by scanning electron microscope and optical analysis of particle images, realistic representative volume elements (RVE) of microstructure are generated taking into consideration the particles circularity and size distributions. Then FE simulations are performed to study the influence of the microstructure and matrix-filler interface conditions on the mechanical properties of the composites. It is assumed that the mechanical behaviour of rubber is non-linear, while the tungstate particles are modelled by a linear elastic material. The FE simulations reproduce uniaxial compression tests. Two types of interface condition between matrix and particles are simulated: A perfect adhesion and absence of adhesion. Corresponding stress-strain curves are constructed. Comparison with experiments shows that the real stress-strain curves for pre-loaded samples path within intervals given by the modelling, i.e. pre-loading leads to partial damage of bonding between matrix and particles.