In this article, we analyze two modified Goubau waveguides at THz frequencies. The first structure is the conical modified Goubau waveguide, where an air gap has been located between the metal and inner surface of the dielectric layer. The electromagnetic fields have been written in various regions and the propagation loss and characteristic equation have been derived for this waveguide. The cylindrical Goubau waveguide with an elliptical cross-section (or briefly called “Elliptical modified Goubau waveguide”) is the second waveguide that has been analyzed by applying the Mathieu functions in the elliptical coordinates. Both structures have been simulated in HFSS software to validate the theoretical results. There is good agreement between simulation and analytical results. Furthermore, the comparison of modified Goubau structures with typical ones, clearly indicates that better field confinement and low propagation loss can be obtained by utilizing the air-gap in the modified Goubau waveguides. These structures can be utilized in multi-channel communications and designing antenna feed at THz frequencies.