In this paper, we present a probabilistic Monte-Carlo method to simulate the electromagnetic field in multiple interface problems based on transmission lines. We present numerical results for the simplest case of the propagation of gaussian pulses and sinusoidal sources in lossy and lossless dielectric slabs which demonstrate the applicability of the method to solve network problem in microwave theory. We also present a methodology to obtain the amplitude and phase associated with every point

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... the domain without resorting to fourier transformations. This method is an important achievement in the development of our Monte-Carlo method because otherwise we would have to integrate the field over time to achieve similar results, which would be unpractical for a Monte-Carlo method. Finally, we compare our results with well established theory to validate the methods.