While the scattering of a plane acoustic wave from a solid isotropic cylinder has been extensively studied for the past several decades, very little has been investigated regarding scattering from anisotropic cylinders. In this paper, the mathematical formulation for the scattering of a plane acoustic wave incident at an arbitrary angle (alpha) on an infinite transversely isotropic cylinder is developed. The normal mode solution is based on decoupling of the SH wave from the P and the SV waves. The resulting partial differential equations have closed-form solutions and the scattered pressure field can be calculated at any point outside the cylinder. The solution degenerates to the well-known simple model for isotropic cylinders in the case of very weak anisotropy. The validity of the mathematical model is verified first by applying it to the familiar case of an isotropic aluminum cylinder. The model is then applied to a transversely isotropic cylinder generated by perturbing various elastic constants of the isotropic aluminum cylinder. The manner in which these perturbations affect each of the Rayleigh, Whispering Gallery, and longitudinally guided wave modes is shown to be consistent with elasticity theory and modal shapes of these resonances. Some experimental results are also presented.