The scope of the present work is the application of a particular class of strain energy function, based on the logarithmic strain, for the prediction of the twisting moment and axial force of a rubber circular cylinder under combined extension and torsion. The strain energy function involves four material parameters three of which are determined by fitting Published experimental data from simple tensile and compression tests of natural rubber. One of the parameters of the proposed model has physical meaning, and it is equal to one ninth Of the initial modulus of elasticity of the material. Hence, the number of unknown parameters is reduced to three. The logarithmic strain energy function is then applied to a combined extension and torsion problem of a rubber circular cylinder to check its performance for more complicated deformations. The results are compared with corresponding experimental and theoretical solutions available in the literature to validate the proposed model. It is found that the proposed strain energy function apart from predicting the common modes of deformations is also capable to determine more complicated types of deformation. (c) 2008 Wiley Periodicals, Inc.