The modeling of the viscoelastic behavior of rubber-like materials is an important challenge due to its non-linear properties.It has a great impact on the performace of tires and seals. We present a force-displacement based approach utilizing fractional derivatives to include the materials viscoelasticity. Therefore we show the resulting equation of motion, incorporating a fractional element to take the materials damping into account. The resulting fractional derivatives are calculated using the Grunwald definition. To apply this approach in structural dynamics, we also outline the combination of the fractional equation of motion with the unmodified Newmark integration scheme.The resulting framework allows the study of viscoelastic structures in the transient domain. To reduce the calculation costs, the structural model is also reduced while maintaining the fractional viscoelastic material behavior. The resulting model is applied to a tire tread block.