Rubber-like materials deform largely and nonlinearly under loading and preserve their initial configuration after removal of the load. These materials are usually modeled as being homogeneous, isotropic, and incompressible elastic solids that are supported by experimental data. In this article, a general form for the strain energy density of these materials is assumed as the sum of two independent functions of the first and second strain invariants. Applying the essential requirements on the form of the strain energy density, the mathematical form of these functions is obtained as polynomial, logarithmic, and exponential. Then a general form is derived for the strain energy density of compressible materials and its effectiveness is evaluated for hydrostatic compression and uniaxial tension tests. The determination of material parameters and the evaluation of effectiveness of models are done based on the correlation between the values of the strain energy density (rather than the stresses) cast from the theory and the test data. Comparison of the theoretical predictions with the experimental data indicates that the represented models can achieve a satisfactory agreement with the behavior of different materials. POLYM. ENG. SCI., 56:299-308, 2016. (c) 2015 Society of Plastics Engineers