An accurate selection of strain energy function (SEF) plays a very important role for predicting the actual behavior of rubber material in the finite element analysis (FEA). The common method for selecting the SEF is by using the curve fitting procedure. However, the behavior of some typical rubbers, such as low grade rubbers (average hardness value of 47.2), cannot be predicted well by only using the curve fitting procedure. To accurately predict the actual behavior of such specifically nearly incompressible material, a series of FEA were carried out to simulate the actual behavior of four physical testing materials, namely the uniaxial, the planar shear, the equibiaxial, and the volumetric tests. This FEA is intended to examine the most suitable constitutive model in representing the rubber characteristics and behavior. From the comparisons, it can be concluded that the Ogden model provides a reasonably accurate prediction compared to the remaining investigated constitutive material models. Finally, the appropriate SEF, i.e. the Ogden model, was adopted for modeling a low-cost rubber base isolator (LCRBI) in the finite element analysis (FEA). The simple uniaxial compression test of the LCRBI is required for validating that the selected SEF works for predicting the actual behavior of LCRBI.