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This article presents guided-wave scattering by defects in a plate with finite width. The system comprises a homogeneous, isotropic, linearly elastic plate containing defects. The wave scattering is solved by a boundary element method (BEM) with radiation conditions for scattered guided waves. For the radiation conditions, the scattered waves are expressed by modal expansion using the semi-analytical finite-element (SAFE) dispersion analysis method. This study proposes a simple SAFE-BEM formulation based on the Galerkin projection with guided-wave mode structures accommodating beam solutions as the incident wave. The scattered waves are evaluated as far-fields in an infinite plate to consider the scattered far-fields in the framework of two-dimensional (2D) plate-wave theory. Numerical results demonstrate that the proposed SAFE-BEM formulation provides sufficiently accurate solutions. The present treatment of incident and scattered waves suggests that the 3D wave scattering in a plate with finite width can be examined using the framework of 2D plate-wave theory. [Display omitted] • A simple hybrid SAFE-BEM formulation is proposed. • The Gaussian beam of a plate wave is the incidence. • Scattered far-fields are evaluated based on 2D plate-wave theory. • 3D scattering is examined in the context of the 2D theory framework. [ABSTRACT FROM AUTHOR]