In this paper, the static and dynamic stiffness of rubber subjected to compression and shear are investigated for rubber bearing applications. For static stiffness, existing models to describe the rubber behaviors are based on linear elasticity and assumptions which may not be adequate during excessive deformation. In the first part of this paper, by modeling rubbers as hyperelastic materials and utilizing finite element analyses, key assumptions of the classic formula are first examined and the rubber behaviors in compression and shear are then simulated. It is found that the classic formula underestimates the stiffness of the rubber. In particular, for rubber with high shape factors, the compression to shear stiffness ratio could deviate considerably from the classic relation at typical working strain levels and this could significantly affect machine performance prediction and design. On the other hand, due to the viscoelastic nature, the dynamic stiffness of rubber bearings varies with working frequencies, affecting precision control. In the second part of this work, rubber pads are modeled as three-parameter general Maxwell fluids for dynamic stiffness evaluation. By combining the original rubber bearing with an additional elastic flexure or even a secondary rubber, it is possible to change the original rubber stiffness in both the compression and shear directions. Finally, designs to reduce high frequency shear stiffness or to enhance the steady state compression stiffness of rubber bearings are proposed and demonstrated.