An elastomeric material was investigated with a bubble inflation rheometer, and its mechanical behavior was modeled as a rubber-like solid. Classical strain energy functions were considered and the hyper-elastic constants were calculated by a direct identification procedure from simple uniaxial and equibiaxial extension test data, and the results are compared against those obtained by an inverse method from bubble inflation test data. The latter amounted to minimizing a cost function and matching the measured response to a finite element analysis solution, which depended on the unknown material parameters. The optimization employed the Levenberg-Marquardt algorithm and Abaqus software to compute the cost function and its gradients. The constants so obtained were further used in finite dement analysis, and the numerical results were compared with experiments. This study showed that the inverse method, used to estimate the material parameters, is a good alternative to the direct identification, especially since the latter often requires homogeneous strain state, which is very difficult to obtain.