Characterization of the mechanical properties of human-tissue-mimicking silicone elastomers is important for producing accurate tissue models for experimentation. However, the viscoelastic and frequency-dependent material properties of elastomers are difficult to quantify. We present a material characterization technique for a silicone elastomer used to mimic human soft tissue based on generalized-Maxwell-type material models with and without fractional dissipating mechanisms. The silicone specimens were prestressed and had the shape of cylindrical rods. It was possible to consistently identify material properties of all specimen samples from different batches of the material obtained from the manufacturer. As a general trend, material models with a higher number of parameters performed better, with the exception of models with fractional order damping mechanisms. Fractional models had the highest success for nearly all the samples in representing the dynamic behavior of the elastomer in the frequency range of 5-100 Hz, where the specimen structure displays a strong modal response.