There have been many papers about applications of substrate integrated waveguide (SIW). Only a few related to the use of mathematical methods to analyze SIW, however, were reported. We present an analytical method that is easy, quick and also accurate to obtain the modal dispersion diagrams and field distributions of SIWs. The closed-form characteristic equations and field expressions provide us insights into the modal behavior of the SIW, providing us the knowledge of the impact and influences which the various parameters have on the SIW, thereby saving a great deal of time in engineering and design often entailing lengthy simulations by full-wave solvers or even trial-and-error practices. We compare the dispersion diagrams and modal field distributions obtained by using our analytical method with those generated by CST Microwave Studio.