The paper presents a proposal of using an experimental phenomenological approach and energy based method to the modelling of mechanical properties of nonlinear elastic mate- rials using examples of two selected polymers. On the basis of an experimental stress-strain relation, together with transversal deformation measurement and the geometrical interpre- tation of the deformation process, analytical forms of the strain energy density function and a pure volumetric part of the strain energy density function have been introduced. The volumetric part of energy has been used in the description of the material damage process interpreted as the appearance of the first plastic deformations, which is the original part of the work and continuous investigations carried out by Wegner and Kurpisz. All theoretical investigations have been illustrated using examples of PVC and PA-6.