The problem formulation for scattering of a plane time-harmonic longitudinal wave by a cylindrical inclusion in a homogeneous, isotropic, linearly elastic solid is reduced to the solution of a system of singular integral equations over the inclusion-matrix interface. The inclusion is circular cylindrical with semi-spherical end sections. The singular integral equations are solved by the boundary element method. Once the interface fields have been determined, the scattered far-field is obtained by the use of elastodynamic representation integrals. Of particular interest is the scattering cross-section. The results can be used to determine the attenuation of a longitudinal wave propagating in a solid with a dilute random distribution of whiskers of the shape analyzed in this paper.