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The transmission and reflection of guided acoustic waves by a transverse boundary separating two isotropic plates has been studied by two numerical methods, viz. the pointmatching (collocation) method and the least‐squares boundary residual method. In both cases, normal mode expansions are made on both sides of the interface, and both propagating and evanescent modes are used to match the usual boundary conditions along the boundary. The plate thicknesses are chosen sufficiently large that the lowest‐order modes correspond very closely to Rayleigh waves and hence information is gained about the reflection and transmission of Rayleigh waves at material discontinuities. We have investigated the influence of the material properties and plate thicknesses on the guided wave reflection and transmission coefficients, as well as the conversion efficiency into higher order guided wave modes that approximate the bulk waves that would be excited in the two semi‐infinite media case.