In this paper, rectangular wave guides have been analyzed using a square wave incidence which can be used for digital communicat ion techniques . The E 1/mnmode of propagation is solved using Eigen functions taking transverse propagation constant in different regions of dielectric waveguide and then the characteristic equations have been derived. The characteristic equations are solved graphically by mode matching inside and outside fields of waveguide. The normalized propagation constant so obtained, for square wave incidence is compared with the sinusoidal wave obtained by Marcatili method and other methods. The results match fairly well at frequencies near the cut-off of dielectric waveguide.