The development of a constitutive model to describe the dynamic response of a filled rubber compound is presented in this paper. A series of cyclic tension tests were done on the rubber compound with mean strains ranging from 0.2 to 0.5, strain amplitudes ranging from 0.05 to 0.2, and strain rates ranging from 0.1 to 10 s−1. The cyclic strain-controlled test results showed material rate dependence and hysteresis, and this motivated the development of a phenomenological-based, hyper-viscoelastic constitutive model. A Zener model, i.e., a spring in parallel with a Maxwell element, was assumed. The total stress was decomposed into a rate-independent equilibrium stress and a rate-dependent overstress. The springs were modeled as neo-Hookean, while the damper was defined by a nonlinear viscosity function. Material constants for the constitutive model were calculated from the cyclic tension test results. Cyclic tension tests were also performed on a sheet with central hole to check the accuracy of the constitutive model. The constitutive model was implemented into ABAQUS Standard with a user-defined material subroutine. The finite element analysis simulation of the rubber sheet with a central hole demonstrated relatively good agreement with the experimental data.