A family of hyperelastic finite elements capable of modeling arbitrarily large strains for axisymmetric and plane strain analyses has been developed. Constitutive behavior is determined by the selection of a strain energy density function for which user-supplied coefficients are required. Selective reduced integration for the volumetric strain energy terms allows for successful modeling of nearly incompressible materials. Available strain energy density functions are as follows: Mooney-Rivlin, Blatz-Ko, power law, and a nine-term Mooney expansion. The Ogden Strain Energy (OSE) law has also been implemented. The OSE law defines the strain energy relationship entirely in terms of the three principal components of stretch. This differs from the approach of other strain energy formulations, such as the Mooney law in which the strain energy is written as a function of strain invariants. The OSE law as implemented in this formulation is designed to facilitate the user's task of converting physical test data to the numerical (algebraic) form required for input. The family of hyperelastic finite elements has been integrated into ANSYS Revision 4.2 via the user element interface. Numerous verification solutions have been performed. As a representative example, a comparison with a closed-form solution for a Mooney-Rivlin type material is presented. Finally, the difficulties of obtaining test data in the form of user-supplied constants is discussed in the context of the comparison of experimental measurements and analytical simulation of an elastomeric test specimen.