In this paper, an explicit acoustical wave propagator technique is introduced to describe thetime-domain evolution of acoustical waves in two-dimensional plates. A combined scheme withChebyshev polynomial expansion and fast Fourier transformation is used to implement theoperation of the acoustical wave propagator. Through this operation, the initial wave packet at t50 is mapped into the wave packet at any instant t.0. By comparison of the results of the exactanalytical solution and the Euler numerical method, we find that this new Chebyshev–Fourierscheme is highly accurate and computationally effective in predicting the acoustical wavepropagation in thin plates. This method offers an opportunity for future study of dynamic stressconcentration and time-domain energy flow in coupled structures. © 2004 Acoustical Society ofAmerica.