We discuss the development of a method for the determination of the material properties of rubber and rubberlike materials within the context of a novel constitutive framework that has been put into place recently. The new constitutive framework leads to fewer material moduli than the models that are currently in vogue. We corroborate the predictions of our model against the experimental data of Treloar as well as Jones and Treloar for uniaxial and biaxial loadings and also with regard to new experimental results that have been generated by us for uniaxial stretching of natural rubber. We record both the axial and lateral responses of the specimens. This allows us to also examine the compressibility of the natural rubber specimens. Finally, we also characterize the response of compressible elastic bodies both under the assumption that the motion is isochoric, as the experiments suggest insignificant change in volume, as well as without resorting to such an assumption, when subjected to biaxial loading.