Transient ultrasonic guided waves in anisotropic bi‐layered plates with finite‐width are investigated in this paper. Composite bi‐layered plates consisting of GaAs substrate coated with Nb sheath is considered as an example because of its application to electronics and calorimetry. The purpose is to investigate the acoustic mode coupling (“pinching”) phenomena for phonon transport. A semi‐analytical finite element (SAFE) method is adopted to study the guided wave dispersion behavior in finite‐width elastic plates. Nine‐noded quadrilateral elements are used to model the cross section of the finite‐width plate. Propagation in the axial direction is modeled by analytical wave functions. Elastodynamic Green’s functions are derived using modal summation in the frequency‐wavenumber and time‐space domains. Results for dispersion and transient analysis of guided waves in finite‐width plates are presented and compared for different aspect ratios. Group velocities are calculated and wave arrival times are computed for different plate cross sections as well as different excitation frequency. Numerical results show significant influence of the plate aspect ratio on the dispersion and transient wave response. Complex nature of quasi‐mode dispersion and propagation due to pinching phenomena in anisotropic plates require such quantitative analysis to afford easy interpretation. These results would be important for nondestructive material evaluation and for characterization of phonon transport in anisotropic bi‐layered plates. © 2004 American Institute of Physics