The Interaction of electromagnetic waves with dielectric bodies and metals has been extensively studied because of its importance to problems including propagation through rain or snow, scattering by and detection of air borne particles, coupling to missiles with plasma plumes or dielectric-filled apertures, performance of communication antennas in the presence of dielectric and magnetic inhomogeneities, and medical diagnostics and power absorption in biological bodies. Computational electromagnetics methods (CEM) offer and indispensable tool for calculating the electromagnetic scattering from an internal field distribution of arbitrarily shaped, inhomogeneous, dielectric bodies. The aim of this thesis is the study and simulation of a RF coils system design by developing a novel parallel fast Method of Moments (MoM) modeling approach suitable for the simulation of dielectric bodies and metals. The parallel fast MoM implementation uses volume and surface basis functions with special properties appropriate for the representation of flux current densities for perfect electric conductors (PEC) and dielectrics. The results obtained with our modeling method were confirmed by comparisons with analytical solutions and other commercial software results, yielding very good agreement. The RF coil is employed in high field Magnetic Resonance Imaging (MRI) to obtain high quality brain images. Among all the clinical imaging techniques, MRI stands as a noninvasive technique that provides accurate, detailed anatomic images, which has had a major impact in the diagnosis of human diseases. MRI is a widely use soft-tissue imaging modality that has involved over the past several years into a powerful and versatile medical diagnostic tool capable of providing in-vivo diagnostic images of human anatomy. Current research areas in MRI system design are driven by the need to obtain detailed high resolution images with improved image signal-to-noise ratio (SNR) at a given magnetic field strength. One of the most critical factor that influences the quality and resolution of the MRI is the homogeneity of the RF field. To this end, this requirement demands the development of high performance MRI radio frequency (RF) coils and a standard procedure for enhancing the uniformity of the field directly at the modeling stage of the RF Coil.