In this work, the author implements concepts and methods of analysis of nonlinear elasticity theory in a simplified description of elastic-plastic properties of materials. Taking the principle of conservation of energy as the theoretical basis, the author formulates a criterion that makes it possible to examine the stability of internal equilibrium in deformed material whose nonlinear properties are defined by strain energy density function. The formulae allowing for assessment of complex states of strain in the aspect of material strength were derived on the assumption of small deformation. These formulae can replace mathematical relationships traditionally known as strength hypotheses. The example included in the paper presents the method of determining, in the space of strain state components, the areas where permanent deformation or destruction of material is possible because of strain state stability. Characteristic parameters used in the example are obtained in a static tensile test on specimen 01· constructional carbon steel of ordinary grade. The results of the analysis, based on the formulated strength hypothesis on stability of strain state, are compared with those resulting from the Huber's hypothesis on energy of non-dilatational strain.