The paper is focussed on numerical simulations of the fracture of a quasi-brittle specimen due to its impact onto a fixed rigid elastic plate. The failure of the specimen after the impact is modelled in two ways based on the physical discretization of continuum: via physical discrete elements and pseudo-particles. Advantages and drawbacks of both used methods are discussed. The size distribution of the fragments of the broken specimen resulting from physical discrete element model simulation follows a power law, which indicates the ability of the numerical model to identify the fractal nature of the fracture. The pseudo-particle model, on the other side, can successfully predict the kinematics of the fragments of the specimen under impact failure.