Rubberlike materials are characterized by high deformability and reversibility of deformation. From the continuum viewpoint, a strain energy density function is postulated for modeling the behavior of these materials. In this paper, a general form for the strain energy density of these materials is proposed from a phenomenological point of view. Based on the Valanis-Landel hypothesis, the strain energy density of incompressible materials is expressed as the sum of independent functions of the principal stretches meeting the essential requirements on the form of the strain energy density. It is cleared that the appropriate mathematical expressions for constitutive modeling of these materials are polynomial, logarithmic, and particularly exponential functions. In addition, the material parameters are calculated using a novel procedure that is based on the correlation between the values of the strain energy density (rather than the stresses) cast from the test data and the theory. In order to evaluate the performance of the proposed strain energy density functions, some test data of rubberlike materials with pure homogeneous deformations are used. It is shown that there is a good agreement between the test data and predictions of the models for incompressible isotropic materials. POLYM. ENG. SCI., 50:1058-1066, 2010. (C) 2010 Society of Plastics Engineers