**Abstract**

A two-Dimensional Finite Element Method of electromagnetic (EM) wave propagation through the soil is presented in this chapter. The chapter employs a boundary value problem (BVP) to solve the Helmholtz time-harmonic electromagnetic model. An infinitely large dielectric object of an arbitrary cross-section is considered for scattering from a dielectric medium and illuminated by an incident wave. Since the domain extends to infinity, an artificial boundary, a perfectly matched layer (PML) is used to truncate the computational domain. The incident field, the scattered field, and the total field in terms of the z-component are expressed for the transverse magnetic (TM) and transverse electric (TE) modes. The radar cross-section (RCS), as a function of several other parameters, such as operating frequency, polarization, illumination angle, observation angle, geometry, and material properties of the medium, is computed to describe how a scatterer reflects an electromagnetic wave in a given direction. Simulation results obtained from MATLAB for the scattered field, the total field, and the radar cross-section are presented for three soil types – sand, loam, and clay.

**Keywords:** electromagnetic signal in soil, finite element method, radar cross-section, underground wireless communication
