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A simple 1-dimensional model is presented to investigate elastic stress waves in composite laminates excited by underwater explosion shocks. The focus is on the elastic dynamic stress fields in the composite laminate immediately after the action of the shock wave. In this model, the interaction between the laminate and the water is taken into account, and the effects of the laminate-water interaction on the stress wave fields in the laminate are investigated. In the formulation of the model, wave fields in the laminate and the water are the first obtained in the frequency domain and then transferred into the time domain using the Fourier transform techniques. A quadrature technique is used to deal with the Fourier transform integrals in which the integrands have very sharp peaks on the integral axis. Numerical examples for stress waves in a steel plate and a glass reinforced plastic sandwich laminate are presented. The technique and the results presented in this article may be used in the design of ship hull structures subjected to underwater explosions.