In this paper, we propose a stochastic model for the resistive switching of ReRAM devices with 1T1R configuration. We work with the fact that the switching occurs in the narrowest zone of the conductive filament due to changes caused by the electric field. This active region is represented by a net of vertical connections, each one composed of three electrical elements: two of them are always low resistive (LR) while the third one acts as a breaker and can be low or high resistive (HR). The breaker can change its state according to a switching probability (Ps), which depends on the voltage drop in the breaker and the threshold voltage, Vset or Vreset for the set or reset process, respectively. This approach gives the model the stochastic behavior and generates the variability observed in the current–voltage curves of most of ReRAM devices. Further, we add another resistor in series in the circuit to represent the electrical signal of the transistor. By comparing measured and simulated IV curves of HfO2-based ReRAM devices of two different scales, nm2 and µm2, we validated the model. The flexibility and straightforward implementation of this resistive switching model make it a powerful tool for studying ReRAM memories and other stochastic devices.