Maxwell's equations are solved in an electro-magnetic rectangular waveguide with the boundary determined by material properties and interface conditions wherein finite point set method approximates the partial derivatives of the scattered fields. The process is time dependent. Waveguide propagation depends on the operating wave length, polarization, shape and aspect ratio of the waveguide. A continuous incident pulse is used to study the electric field pattern and transmission behavior in plain and corrugated waveguides. The waveguide is modeled in a 2D rectangle with incident source at the left boundary. Transmission coefficients are computed as a function of frequency of the continuous pulse for both the plain and corrugated waveguide of various heights λ/2, λ/4 and 3λ/4. © 2013 Elsevier Inc.