Viscoelastic polymer composites are widely used for vibration control in different fields of engineering like aerospace, mechanical, and structural engineering. The viscoelastic properties of these materials are strain rate-dependent and are highly related to frequency. Yet to date, less attention has been paid to quantifying the effects of these parameters and their interactions on damping properties and providing an approximation method for further applications. In the present research, a series of experimental tests was conducted on a viscoelastic material and the experimental data were numerically analyzed in detail. Sensitivity analyses are usually applied to quantify uncertainty using sampling techniques. However, in this study a method was proposed to derive a closed-form solution using the response surface function and a derivative-based global sensitivity analysis to evaluate the output contribution of each parameter. These effects were quantified and several approximation statistics were provided for future engineering implementations. The computational evaluation conducted in this study gives a detailed insight into the mechanical behavior of viscoelastic materials.