A finite element eigenfunction method (FEEM) is formulated for elastic wave scattering by bounded three-dimensional axisymmetric regions (cavity, homogeneous, or inhomogeneous) for harmonic waves incident at arbitrary angles. The solutions are hence three-dimensional and no longer axisymmetric. The scattering region is enclosed within a sphere. The scattered field outside the sphere is expanded in outgoing vector spherical functions. Within the sphere, basis-functions are generated by a finite element technique applying the vector spherical harmonics as boundary conditions. The field inside the sphere is then written as a superposition of these basis functions with unknown coefficients which are then solved by matching with the exterior field. Numerical results are obtained for a variety of scatterers and comparisons made with available results.

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