In this work we present a two-dimensional (2D) model for an organic thin film photo-conductive sensor containing a planar heterojunction and in-plane electrodes. The model simulates the flow of charge carriers based on the standard one-dimensional semiconductor transport and continuity equations, and combines this with a 2D model for the electric field. This procedure results in a hybrid differential/integral equation formulation. We present and analyse simulation results that resemble very well measured current–voltage characteristics of a real sensor under different illumination levels. We find that for currents below a critical value the sensor behaves like a resistor. Above this critical current the current increases much more slowly due to space charge accumulation close to the cathode. We explain the critical current as the maximum reverse current of the solar cell formed by the heterojunction covering the cathodic electrode.