One of the most widespread hypotheses for the origin of the present-day overpressure in the shale Post-Chalk section in the North Sea is the very rapid sedimentation from Neogene to present day. We tested this hypothesis by the means of numerical forward finite elements modelling and successfully simulated the overpressure build-up during the Cenozoic filling of the North Sea with relatively simple model set-up. Our model shows that overpressure of approximately 28% above hydrostatic developed in the Neogene, while during the Quaternary, it reached up to 36% above hydrostatic. At present day, the predicted onset of overpressure starts at about 800–1000 m below seafloor, while the maximum (magnitude about 1.36 sg, i.e. 36% above the normal hydrostatic pressure) is at approximately 2100 m. This overpressure profile fits reasonably well with data from wells drilled in the Central Graben. The exact magnitude of the overpressure depends on the used assumptions, the model set-up and the values of the input parameters. Especially the dynamic interaction between high sedimentation rates, clay permeability and low horizontal pressure gradient seems to be a key factor in the efficiency of dewatering of saturated clays during burial. The results indicate that, the assumption of horizontal stress isotropy results in nearly no horizontal fluid flow, despite the same magnitude for the vertical and the horizontal permeability. In these conditions, the vertical permeability plays much bigger role than the horizontal one in the effective de-watering of the sediments during burial. Further investigation is needed to explore the role of horizontal pressure gradient in fluid migration in passive sedimentary basins.