The concept of the Representative Volume Element (RVE) is analysed in the present paper. For elastic materials, one can determine the size of the RVE. However, for other applications, such as the case of softening materials, the RVE size determination problem can become extremely difficult or, sometimes, even impossible to solve. In the present work the RVE has been investigated for different material behaviour, namely elastic, hardening and softening. Results were based on a statistical analysis of numerical experiments, where tests have been performed on a random heterogeneous material.