This paper presents a rigorous scattering model of an infinite slit on a dielectric-loaded parallel-plate waveguide with an oblique incident TEM wave. The dyadic Green’s functions of an equivalent line source are derived first and then applied to solve the scattered fields in terms of reflection, transmission, and radiation. Special treatment with PEC/PMC symmetry is employed for fast and accurate calculation. The proposed model was carefully validated by the full-wave simulator with excellent agreement. Some interesting scattering phenomena are found and emphasized, as they are crucial in explaining the special features of slit-based planar structures. In this paper, we demonstrate the presented model for the analysis and physical explanation of unique features found in a slitted substrate integrated waveguide, grounded coplanar waveguide, and grounded coplanar stripline. The proposed model provides a simple and effective approach for the design of potential slit-based planar circuits and antennas based on the presented structures in this paper.