In this research the electromagnetic scattering of a plane wave from a two-dimensional cavity embedded in an infinite, perfectly conducting ground plane is investigated. The plane wave is assumed to be under transverse electric (TE) polarization with respect to the x-axis. The cavity may be empty or filled with an arbitrary homogeneous, lossy material. A coupled set of scalar integral equations that govern the electromagnetic scattering is implemented. An approximate solution to the scalar integral equations is found via a Method of Moments (MoM) algorithm. The algorithm is implemented in a computer code, and approximations to the total magnetic field on the cavity surface and aperture as well as the normal derivative of the total magnetic field on the cavity aperture are obtained. These fields are then used to calculate the two-dimensional monostatic RCS signatures of various test cavities. The numerical results from the algorithm are shown to agree well with the RCS signatures calculated by other well-known methods and published results. In addition to being accurate, the algorithm is very computationally efficient. The process results in simply solving a relatively small, well-conditioned matrix system for each incident angle to produce the unknown fields.