The complex dispersion characteristics of the surface wave modes of plasma column loaded closed cylindrical waveguides have been investigated. The numerical results for partially or fully plasma loaded waveguides have been obtained from the Method of Moment (MOM), the exact dispersion equation and the quasistatic dispersion equation. A numerical technique based on the solution of the MoM has been proposed in order to obtain the complex propagation constant from the exact solution. The surface wave modes obtained from these methods have been presented comparatively in the figures. Thus, the insufficiency of the quasistatic approximation to obtain the complex surface wave modes has been shown. Additionally, the study involves a comprehensive literature review including physical descriptions and/or behavior in different physical media of surface wave modes and complex wave modes.