This work deals with the modelling of electrochemical reactors with bipolar electrodes. We give a numerical model which enables us to compute electrical current and potential distributions in an electrochemical cell of any type of geometry in two and three dimensions, including electrodes at an unknown floating potential. We first present electrochemical reactors and particularly insist on kinetics and thermodynamics phenomena responsible on potential discontinuities at electrodes-electrolyte interfaces. Secondly, we derive a complete mathematical model which contains the equations of conservation of the electrical current and the nonlinear conditions at interfaces. This problem is approached and solved using a finite element method for two and three-dimensional systems. A detailed description of approximations we have made and algorithms of numerical solving are then given. Afterwards, the architecture of the software that we have built is detailed and numerical simulations are compared to experimental measurements. Finally, some computation results are presented. Several geometries of different reactors have been simulated with applications in water electrolysis and soils decontamination.