A numerical approach has been proposed to quantify the size of representative volume elements (RVEs) for materials that consist of particles in a matrix material. Various series of random particle distributions with different densities have been generated, which are used as input for nonlinear finite element simulations. A statistical procedure has been used to determine averages and standard deviations for each test series. Several criteria have been taken to quantify the size of the RVE, including peak load, dissipated energy and strain concentration factor. The various criteria lead to different RVE sizes. Furthermore, the sensitivity of these three properties to the particle size distribution is assessed. An investigation is made in which smaller particles in an RVE were replaced by larger ones while the aggregate density distribution was kept constant. Finally, the interaction is studied between the size of the RVE and the internal length scale of the underlying level of observation.