The method of spherical harmonic tensors developed Mark for solving the Boltzmann transport equation in isotropic media is herein extended to anisotropic media for cylindrical geometry. A formal solution is given for the case of two concentric cylindrical media, A and B, but no numerical work has yet been done. The following treatment differs from a similar one by the H. K. Ferguson Co. in that the external medium B is assumed to be both a neutron absorber and finite in extent rather than a non-absorber and infinite in extent.