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This paper presents a series of experimentations and numerical modeling to evaluate the damping of rubber for seismic isolation purposes. A cyclic shear test is considered as a standard procedure to evaluate the damping of rubber materials. However, there is another method to evaluate the viscous damping of rubber by means of relaxation test that requires only small dumb-bell specimens of rubber, using a uniaxial tensile test device. This method allows an efficient procedure in examining the mechanical characteristic of rubber for seismic isolation purposes. This paper evaluates such a procedure to characterize the mechanical properties of a low damping rubber. The result shows that the proposed procedure presents a good prediction of the mechanical properties of the rubber.