In this paper, we present a set of numerical schemes to solve the Muller integral equation for the analysis of electromagnetic scattering from arbitrarily shaped three-dimensional dielectric bodies by applying the method of moments(Mon. The piecewise homogeneous dielectric structure is approximated by planar triangular patches. A set of the RWG(Rao, Wilton, Glisson) functions is used for expansion of the equivalent electric and magnetic current densities and a combination of the RWG function and its orthogonal component is used for testing. Numerical results for a dielectric sphere are presented and compared with solutions obtained using other formulations.