In this thesis a numerical technique is developed determining the propagation constant in waveguides and transmission lines. The technique accounts for both dielectric and conductor losses in a guide having an arbitrary cross section and uses a full-wave solution process. A set of coupled, vector integral equations which characterize the system are derived. The equations enforce the necessary boundary conditions on the tangential electric and magnetic fields at the boundaries separating the conductors and dielectrics. The method of moments (MOM) technique is used to cast the equations into a numerically solvable form. Computed results for various waveguide structures are compared to known or perturbed results for three well-known structures. However, the program is more general and may be applied to other cross-sections. Finally, possible future extensions of the work is presented. / Master of Science