The development and application of a fourth-order Modified Runge-Kutta (MRK) scheme on a transformed coordinate system with Maxwell’s equations are presented here. Maxwell’s equations are the governing equations for modeling electromagnetic wave propagation involving scattering, radiating structures, transmission lines, radar, and non-destructive testing. Due to complex geometries in most problems where the material boundaries are not parallel to the grid axis, the application of finite differencing schemes in physical coordinates becomes nonviable. Therefore, by transforming the arbitrary-shaped structures to a rectangular grid, numerical schemes and boundary conditions can be easily implemented. Numerical results for three cases are presented in this paper. Accuracy of the scheme has been established by comparing numerical results with the exact solution and error distribution plots. In the third case, scattering from the lossless dielectric device where the plane wave source is injected using the total-field/scattered-field (TF/SF) technique has been investigated.