Backward diode and tunnel diode were formerly used in communication systems and now considered obsolete. Recently, because of their ultra-low threshold voltage at reverse bias condition, the backward diode is used as a rectifier diode for ultra-low power energy harvester. Unfortunately, there are few models available for SPICE simulation or any other computation analysis. The challenge of modeling backward diode and tunnel diode is their negative differential resistance (NDR) and result in a high probability of having numerical instabilities. This paper will first investigate several available mathematical models such as the polynomial model and Ray’s Empirical model, then, a less complex SPICE model based on discrete components sub-circuit will be proposed. All the unknown parameters of this proposed model are optimized based on measurement data using the Levenberg-Marquardt (LM) algorithm. This discrete SPICE model can be easily modified to model other elements with similar negative resistance behavior.