The response of a periodic plate‐laminated composite to finite, dilatational stress waves has been investigated both experimentally and analytically. The composite was constructed of ten bilaminates oriented so that the stress wave propagated normal to the plane of the plates. The experimental results were compared to the results of a previous study, to the calculations of two wave‐propagation computer programs, and with a model in which the composite was treated as a homogeneous medium for which a stress‐relaxation relation was assumed. From these comparisons, the effects which influence the form of the stress wave were deduced. For the composite configuration used in this study and at a stress level of less than 12 kbar, the effects are geometric dispersion which includes the resonance resulting from the periodicity of the configuration, debonding, material nonlinearities, and viscosity.