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A numerical method for computing the time response of infinite constant cross-section elastic waveguides excited by piezoelectric transducers was developed. The method combined waveguide finite elements (semi-analytical finite elements) for modeling the waveguide with conventional 3-D piezoelectric finite elements for modeling the transducer. The frequency response of the coupled system was computed and then used to simulate the time response to tone-burst electrical excitation. A technique for identifying and separating the propagating modes was devised, which enabled the computation of the response of a selected reduced number of modes. The method was applied to a rail excited by a piezoelectric patch transducer, and excellent agreement with measured responses was obtained. It was found that it is necessary to include damping in the waveguide model if the response near a ldquocut-onrdquo frequency is to be simulated in the near-field.