A nonlinear rubber material model is presented, where influences of frequency and dynamic amplitude are taken into account through fractional order viscoelasticity and plasticity, respectively. The problem of simultaneously modeling elastic, viscoelastic, and friction contributions is removed by additively splitting them. Due to the fractional order representation mainly, the number of parameters of the model remains low, rendering an easy fitting of the values from tests on material samples. The proposed model is implemented in a general-purpose finite element (FE) code. Since commercial FE codes do not contain any suitable constitutive model that represents the full dynamic behavior of rubber compounds (including frequency and amplitude dependent effects), a simple approach is used based on the idea of adding stress contributions from simple constitutive models: a mesh overlay technique, whose basic idea is to create a different FE model for each material definition (fractional derivative viscoelastic and elastoplastic), all with identical meshes but with different material definition, and sharing the same nodes. Fractional-derivative viscoelasticity is implemented through user routines and the algorithm for that purpose is described, while available von Mises’ elastoplastic models are adopted to take rate-independent effects into account. Satisfactory results are obtained when comparing the model results with tests carried out in two rubber bushings at a frequency range up to 500 Hz, showing the ability of the material model to accurately describe the complex dynamic behavior of carbon-black filled rubber compounds.