A higher-order geometry modeling technique is presentedfor the solution of volume integral equations (VIEs) involving arbitrarilyshaped inhomogeneous dielectric structures. Conformal basis functions definedin curved hexahedral finite elements are used to develop a moment method solutionof the VIE. Results are compared with available analytical solutions, andthe method is shown to deliver higher accuracy using coarser meshes as comparedto partial differential equation solvers.