Abstract: The accurate material parameters of hyperelastic constitutive models are the critical factors for the precision assurance of structural finite element calculation for rubber components. Three basic types of mechanical tests, including uniaxial simple tension (ST), planar tension (PT) and equibiaxial tension (ET), were conducted on carbon black filled rubber, and based on these test data, the fitting abilities of six often used hyperelastic constitutive models were investigated. The prediction performances of these models and the model selection strategies were explored in the case of the incompletion of the three basic types of mechanical tests. It is shown that, in order to accurately describe the large and complex deformation behavior of rubber materials, constitutive model selection strategies should be varied with the combination of the mechanical test types. In the case of complete data under ST, PT and ET tests, Ogden model (N=3) is the first choice, and the Yeoh and Arruda-Boyce model are the substitutive ones. If there are only two types of basic tests available, ET test is preferred, and the Ogden model (N=3) is the best model that can precisely predict the third deformation mode. The Arruda-Boyce model provides most excellent prediction for PT and ET deformation based on the ST test data only.