Tantalum-oxide-based bi-layered resistance-change memories (RRAMs) have recently improved greatly with regard to their memory performances. The formation and rupture of conductive filaments is generally known to be the mechanism that underlies resistive switching. The nature of the filament has been studied intensively and several phenomenological models have consistently predicted the resistance-change behavior. However, a physics-based model that describes a complete bi-layered RRAM structure has not yet been demonstrated. Here, a complete electro-thermal resistive switching model based on the finite element method is proposed. The migration of oxygen vacancies is simulated by the local temperature and electric field derived from carrier continuity and heat equations fully coupled in a 3-D geometry, which considers a complete bi-layered structure that includes the top and bottom electrodes. The proposed model accurately accounts for the set/reset characteristics, which provides an in-depth understanding of the nature of resistive switching.