This paper applies the acoustical wave propagator technique to wave packet propagation in a one-dimensional stepped beam. The time-domain analytical solutions of this structure subjected to an initial-value problem with the specific Gaussian waveform were derived and compared with the predicted results obtained by the acoustical wave propagator technique. It is shown that this technique is efficient and accurate in predicting wave propagation in one-dimensional structure with thickness discontinuity. The effects of near-field waves on reflection and transmission coefficients, and transmission efficiencies are also studied in detail. Furthermore, an experiment was carried out to investigate the reflection and transmission of flexural waves in a stepped beam structure. (c) 2006 Elsevier Ltd. All rights reserved.