The mechanical properties of biomaterials under different strain rates play an important role in their application as potential implant material for replacement and repair of soft tissues, that is, liver and kidney. The biomaterials being implanted for the human soft tissues should have the physical and mechanical properties as close as possible to those of the tissues being replaced. Polyvinyl alcohol (PVA) is a biocompatible biomaterial with suitable mechanical properties which is in widespread use in biomedical and pharmaceutical areas as well as in tissue engineering applications. However, so far the effect of strain rate on the mechanical properties of this versatile biomaterial remains poor. In this study, the nonlinear mechanical behavior of a fabricated PVA sponge is investigated experimentally and computationally under different strain rates. A series of tension tests with the strain rates of 1, 20, and 100 mm/min are carried out for the PVA sponge. The Yeoh strain energy density function (SEDF), which is indicated to be the most suitable material model for spongy biomaterials, is calibrated using the experimental data. The general prediction ability of Yeoh SEDF is verified using finite element simulations of PVA tensile experiments. The elastic modulus and maximum stress of PVA sponge with the strain rate of 20 mm/min are almost 48 and 3.22 times higher than that of 1 mm/min. Results also revealed that Yeoh materials model can suitably capture the nonlinear mechanical behavior of PVA sponge biomaterial which can be used in future biomechanical simulations of the spongy biomaterials. These results can be utilized to understand the nonlinear mechanical behavior of PVA sponges and has implications for wound healing and tissue engineering purposes.