Hybrid Substrate Integrated Non Radiative Dielectric Slab Waveguides are proposed as a new guiding structure suitable for mm-wave components. The proposed structure is a combination of two well-known guiding structures, each of which has its wide variety of applications but in different regimes of operation. The combination of the two guiding mechanisms in one physical structure gives unique characteristics to the resulting hybrid waveguide. A systematic analytical way is presented in this paper to characterize the new waveguide in terms of its dispersion relation, modes of operation, field solution, bandwidth of single mode operation, and power handling capability. Some possible applications and design recipes are discussed.