Closed form expressions for the electromagnetic fields in homogeneous anisotropic media are derived in terms of the circular cylindrical vector wave functions for isotropic media. An analytical solution is obtained for the problem of scattering by an infinite homogeneous anisotropic circular cylinder for an obliquely incident plane wave of an arbitrary linear polarization. Numerical implementation and convergence behavior of this solution is discussed. Numerical results for some special cases are compared with existing data. We also present numerical results for the more general anisotropic material case in both graphical and tabular forms. The formulation of this article can be easily generalized to the cases of more complex cases, such as other complex media cases whose eigenwave numbers and eigenwave vectors can be determined, layered structures cases, and multiscatterers cases. ©1997 American Institute of Physics.