A method based on energy is a very useful tool for description of mechanical properties of materials. In the current paper, on the base of geometrical interpretation of a deformation process, the strain energy density function for isotropic nonlinear materials has been constructed. On account of hydrostatic interpretation of the volumetric deformation, the elastic part of energy has been extracted. The initiation of the damage process due to plastic flow of the material under plane stress has been determined and the stability conditions have been formulated by using in the stability analysis the strain energy density function in addition to Sylvester’s theorem and assumption of zero volume change during pure plastic deformations. This concept is an original part of the work and continuation of the investigations previously carried out by Wegner and Kurpisz. The theoretical investigations have been illustrated on the example of aluminium.