Acoustoelastic guided wave, combining the advantages of acoustoelastic effect and guided waves, provides a promising technique in measuring or monitoring prestress. However, computations of the acoustoelastic guided wave are mostly limited to simple waveguides (e.g. plates and rods) and only take account of normal stress. In this paper, a method is proposed to calculate the acoustoelastic guided waves in waveguides with arbitrary cross sections subjected to an inhomogeneous prestress through combining the semi-analytical finite element (SAFE) method and the acoustoelastic effect. The method is first validated in plates with solutions from superposition of partial bulk wave (SPBW) method and then applied to practically important cases to show capacity of the method. This method can also be extended to calculate acoustoelastic surface waves including Rayleigh wave and Love wave using perfectly matched layer (PML) to simulate the semi-infinite half-space where the response of the surface wave to the depth-varying prestress can be investigated which may provide the potential to reconstruct the depth profile of near-surface residual stress from the dispersion data of ultrasonic surface waves.
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