The development of a new strain energy function for hyperelastic solids based on the logarithmic strain measure is the objective of the present article, For all possible types of deformation it was shown that the proposed energy function is based on three independent material parameters, Using available experimental data for rubber-like materials from the literature, one may determined the materials parameters by a nonlinear fitting. The available domain of the strain energy function can be determined by plotting the third invariant of logarithmic strain vs the second one, The numerical integration of the experimental data of true stress as a function of the logarithmic strain for various types of deformation yields the strain energy function W, for rubber-like solids, The proposed model involves only one parameter that must be determined by fitting with the experimental data,