The traditional volume electric field integral equation (IE) used for solution of full-wave scattering problems on penetrable scatterers of arbitrary cross section and its magnetostatic counterpart commonly utilized for the resistance and inductance extraction problem are reduced to a novel derivative-free single-source surface IE. The reduction of volume to surface IE is based on representation of the electric field in the cylinder cross section in the form of a single-layer ansatz. Substitution of such surface based electric field representation into the volume IE reduces it to a surface IE with respect to the unknown surface current density. Since the new surface IE enforces exactly the field continuity at the material interfaces, the radiation condition as well as underlying Helmholtz equations both inside and outside the penetrable cylinder, it is rigorously equivalent to the solution of Maxwell’s equations. The method of moments discretization of the new IE is shown to produce an error-controllable field approximation. Due to the presence of a product of surface-to-volume and volume-to-surface integral operators, the discretization of the novel surface-volume-surface IE requires both surface and volume meshes.