An analysis of acoustic waves in viscoelastic materials reveals that the stress relaxation function for such materials can be evaluated from acoustic dispersion data. In this paper we illustrate this method by evaluating the longitudinal stress relaxation function for the solid polymer, polymethyl methacrylate (PMMA) using previously reported acoustic data. From this result, we deduce the relaxation function appropriate for describing the shock wave response of PMMA by specifying the time‐scale characteristic of plate impact experiments. This relaxation function compares well with the function determined from the experimental observations of steady shock waves in PMMA.