A numerical method is presented for the accurate determination of the viscoelastic spectra from dynamic response function data. First, the technique is validated by application of the method to dynamic data for a hypothetical polymer with an assumed relaxation spectrum. It is shown that the method produces a single retardation spectrum which when used in viscoelastic integral equations yields excellent agreement with the functions from which the spectrum was determined in the first place. Also, upon applying computed transient functions to the linear viscoelastic convolution integral, excellent agreement is obtained. Finally, the method is applied to dynamic mechanical data for a vinyl ester resin system. It is shown that a single retardation spectrum can be generated that upon integration in appropriate integral equations yields response functions in excellent agreement with experiment.