A mathematical model is developed to describe the scattering of a plane wave incident at an arbitrary angle on a transversely isotropic cylinder imbedded in a solid elastic matrix. The model is based on the normal mode expansion method, and accommodates both compression and shear waves, polarized in any direction. The geometry is a good model for a composite material featuring a single reinforcing fiber encased in an elastic matrix. The sensitivity of the system to perturbations in the cylinder’s elastic constants in explored, as revealed by changes in the scattered wave spectrum. The results indicate several system resonances, each sensitive to perturbations in certain elastic constants of the cylinder. Also, dispersive pseudo-Stoneley waves that travel on the matrix-cylinder interface lead to resonances in the scattered wave spectrum that would be good indicators of deficiencies in the integrity of the interface. ©2000 American Institute of Physics.