The hypothesis of strain equivalence is used to measure damage in materials. The physical meaning of the elastic modulus of damaged materials defined in the hypothesis is discussed in this paper. The inapplicability of the hypothesis to be used to determine the damage and its evolution in elasto plastic materials are analyzed. It is emphasized that the method in which the relaxed modulus is taken as the deformed modulus, i.e. the elastic modulus defined in the hypothesis, is only applicable for measuring the damage in elastic materials. A new damage variable is proposed, which is applicable for both elastic and elastoplastic materials. The hypothesis of strain equivalence is used to measure damage in materials. The physical meaning of the elastic modulus of damaged materials defined in the hypothesis is discussed in this paper. The inapplicability of the hypothesis to be used to determine the damage and its evolution in elasto plastic materials are analyzed. It is emphasized that the method in which the relaxed modulus is taken as the deformed modulus, ie the elastic modulus defined in the hypothesis, is only applicable for measuring the damage in elastic materials. A new damage variable is proposed, which is applicable for both elastic and elastoplastic materials.