The development of a spectral domain method of moments code for the modeling of single layer microstrip patch antennas is presented in this thesis. The mixed potential integral equation formulation of Maxwell's equations is used as the theoretical basis for the work, and is solved via the method of moments. General-purpose graphics processing units are used for the computation of the impedance matrix by incorporation of quasi-Monte Carlo integration. The development of the various components of the code, including Green's function, impedance matrix, and excitation vector modules are discussed with individual test cases for the major code modules. The integrated code was tested by modeling a suite of four coaxially probe fed circularly polarized single layer microstrip patch antennas and the computed results are compared to those obtained by measurement. Finally, a study examining the relationship between design parameters and S₁₁ performance was undertaken using the code.