In this work, a model for the resistive switching of ReRAM devices that considers the electrical signal of the measurement element is developed. This model works for bipolar devices that have filamentary-type conduction and it is based on the circuit representation of the conductive filament (CF). The stochastic nature of the switching process, observed in experimental data, has been included by using a switching probability to control CF changes, and therefore, the ReRAM's state. For calibration, the analysis of current-voltage curves of devices of six different areas (nm2range) has been done. Good agreement between the experimental results and the model simulation were found.