© 2018 Author(s). A simulation tool based on a 3D kinetic Monte Carlo algorithm has been employed to analyse bipolar conductive bridge RAMs fabricated with Cu/HfOx/Pt stacks. Resistive switching mechanisms are described accounting for the electric field and temperature distributions within the dielectric. The formation and destruction of conductive filaments (CFs) are analysed taking into consideration redox reactions and the joint action of metal ion thermal diffusion and electric field induced drift. Filamentary conduction is considered when different percolation paths are formed in addition to other conventional transport mechanisms in dielectrics. The simulator was tuned by using the experimental data for Cu/HfOx/Pt bipolar devices that were fabricated. Our simulation tool allows for the study of different experimental results, in particular, the current variations due to the electric field changes between the filament tip and the electrode in the High Resistance State. In addition, the density of metallic atoms within the CF can also be characterized along with the corresponding CF resistance description.