The normal mode expansion technique is applied to the transformed mono-energetic integral transport equation to develop a solution for the rotationally invariant and axially infinite critical two-region cylinder with a finite outer reflector boundary. The model assumes isotropic scattering and identical neutron mean-free-paths in the core and reflector regions. The solution in terms of singular integral equations is obtained by applying a completeness theorem found for the singular eigenfunctions. Numerical results for a variety of core and reflector multiplying properties and reflector thicknesses are presented and compared with the results of other methods. The completeness inherent in this solution and the high precision in the numerical calculations provide results which may be used as analytic standards for this problem. 112