The aim of this paper is to contribute to the prediction of the failure of materials (ductile and brittle) with a single criterion (rule) not violating the assumptions of continuum mechanics. In this work, the failure behavior of isotropic materials is connected with the ability of a material to store elastic strain energy from the very start of loading until its fracture. This elastic strain energy is known that is separated in a distortional and a dilatational part. So, when one of these quantities takes a critical value, then the material fails either by slip or by cleavage. The behavior of a material is described with regard to the secant elastic moduli depending on both unit volume expansion Θ and equivalent strain . This dependence enlightens, in physical terms, the different reaction of materials in normal and shear stresses. T-criterion is applied for the prediction of failure in a series of experiments that took place to an aluminum alloy (Al-5083) and to PMMA (Plexiglas). A single criterion was used for two totally different materials and the predictions are quite satisfactory. This work is a step toward the direction of using one criterion in order to explain and predict failure in materials independently of the plastic strain that developed before fracture.