In this paper, the propagation of EM Gaussian pulse through containers was numerically simulated using the method of characteristics (MOC) in two dimensions where the container has a circular cross-section, may be made of dielectric or magnetic material, and may hold dielectric or magnetic liquid. The MOC approach is used to directly approximate the time-domain Maxwell's equations in a modified O-type grid system. The electric fields sampled at the center of container were shown and compared in a side-by-side fashion. The effects on the electric fields of the following factors were examined: the thickness and material of the container and the liquid inside. The corresponding frequency domain information was obtained through the application of the Fourier transform and compared. To demonstrate the propagation of EM pulse in the modified O-type grid system, the electric field distributions over the whole computational domain for several cases were also presented.