Abstract: Two-dimensional scalar equation of displacement for the cross--plane shear elastic waves in homogeneous and transversely isotropic media like unidirectional fibrous composites is derived. Then, through a simple coordinate system tranform, the scalar equation is standardized into a Helmholtz equation. Integral equations are derived for the scattering problems and boudary element method is used to calculate the scattered cross-plane wave fields by circular cylinders in transversely isotropic media numerically. A discussion is given on the results which is mainly focused on the influence of the anisotropy to the directivity of the scattered fields by circular cylindrical voids.