This paper investigates the use of phenomenological models of viscoelasticity to simulate ultrasonic compression wave propagation in a curing thermoset. Kelvin‐Voigt and Maxwell models do not give physical results whilst the anelastic solid (Debye) formulation and its Cole‐Davidson (CD) extension provide a qualitative match to experiment, although with some inconsistencies. The CD model when fitted to experimental phase velocity data gave parameters that could be used to track molecular polydispersity in the curing thermoset. © 2003 American Institute of Physics