The stress-strain relationships of a rubber material in uniaxial tension, equi-biaxial tension and plane shear loading conditions are tested here. Constitutive parameters in different constitutive models, such as Mooney-Rivlin model, Van Der Waals model and Marlow model can be obtained by least square method using measured and calculated stress-strain relations. The rubber isolators in two rubber mounts are investigated here. Rubber mount I bears stretching/compression deformation or shear deformation, while mount II bears both deformations simultaneously. Using obtained constitutive constants, the rubber isolators’ static stiffness values in three mutually perpendicular directions are calculated, analyzed and compared with their measured results. Based on Mooney-Rivlin model, the effects of these constitutive constants on static stiffness of the two mounts are discussed by comparison. The effects of different models on static force-displacement characteristics of rubber mount I are also analyzed. The conclusion is that it is necessary to choose a relatively accurate constitutive model and appropriate methods for obtaining the model constants in describing rubber characteristic.