For the numerical simulation of acoustic wave propagation in, and the design of acoustic (measurement) systems, the use of reliable material models and material parameters is a central issue. Acoustic material parameters cannot be evaluated based on quasistatically measured parameters, as are specified in data sheets by the manufacturers. At best, rough estimates can be made, which are insufficient for a thorough consideration of acoustic wave propagation, especially in polymers. In this work, a measurement method is presented which quantifies, for a given polymeric material sample, a complex-valued and frequency-dependent material model, taking anisotropy, stress relaxation and creep retardation processes into account. The material samples are designed as hollow cylindrical waveguides. Ultrasonic transmission measurements are carried out between the parallel faces of the sample. To account for the frequency dependency of the material properties, five different transducer pairs with ascending central frequency of 750 kHz to 2,5 MHz are used. Each of the five received signals contains, after passing through the sample, information on the material parameters, on the spatial and spectral excitation of the sample and on the sample geometry, which are separated from each other in an inverse procedure. The solution of the inverse problem is carried out deterministically by iterative comparison of forward simulations of the entire measurement system with the experimentally determined measurement data. For a given solution of the inverse problem, an estimate of the measurement uncertainty of each identified material parameter is calculated.