Transient stress-wave experiments on laminated composites are described, and the results are compared with theoretical predictions. The composites are laminated from alternating layers of high and low-modulus material, which cause a high degree of geometric dispersion of waves propagating in the composite. Experiments were conducted in which waves propagated parallel to the laminations. Flat plates were subjected on one face to a uniform pressure with step-function time dependence induced by a gas-dynamic shock wave. Under this loading, the central portion of the specimen initially responds as if it were laterally unbounded. The average velocity over a 3/8-in-dia area of the backface of the plate was measured with a capacitance gauge. The results are in good agreement with theoretical predictions made with a long-time asymptotic approximation called the head-of-the-pulse approximation. The theory isolates the dominant character of the response and predicts timing and amplitude of oscillations in normalized rear surface velocity within a few percent.