In many applications elastoplastic composites are used in limited amounts, therefore it is important to have estimates of the size of their representative volume element both for modeling and experimental purposes. In this work the tensile response of particle reinforced random composites is simulated by microstructural finite element models. Several microstructural realizations are considered for each composition and volume, and the scatter in the response is used as representativeness metric. The microstructural morphology is characterized using methods and statistical descriptors that can be employed with micrographs of real materials. Numerical results show that the representative volume element dimensions can be estimated by verifying either the consistency of the stress-strain curve for single microstructural realizations and increasing material volume sizes or the convergence of the response of several microstructural realizations at the same material volume size. The analysis of the stress-strain state at the microstructural level shows that the plastic strain and the hydrostatic pressure in the matrix material depend hyperbolically on the interparticle distance. Microstructural analyses show that the matrix coarseness is correlated to the scatter in the mechanical response and therefore can be used to have approximate estimates of the representative volume element size.