The Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE) is a single-source integral equation which can be formulated for solution of radiation and scattering problems on homogeneous as well as piece-wise homogeneous (composite) penetrable objects. The Method of Moments (MoM) discretization of SVS-EFIE produces three dense matrices corresponding to its three integral operators. These operators map the field from the scatterer’s surface to its volume, from its volume to its surface, and from its surface to back its surface. Because of the discretization of both the surface and the volume of the scatterer the resultant dense matrices take large amount of memory and require prolonged computational time, if handled directly. In this work we demonstrate a computational framework based on the theory of hierarchical matrices (H-matrices), which allows to greatly alleviate the CPU time and memory complexity of the SVS-EFIE MoM solution.