Pressure compartments are common in sedimentary basins and are the natural result of the interaction between a number of mechanisms generating overpressures in the subsurface (undercompaction disequilibrium, hydrocarbon generation, and the related processes of oil to gas cracking being the most important ones) and the permeability-related processes that maintain and dissipate those pressures over time. Pressure compartment boundaries within any modelled area are commonly sub-parallel to lithology in a vertical sense. Changes in the permeability of the pressure-sealing sections result in differing rates of pressure bleed-off in the underlying units. In a horizontal direction, faults often act as pressure compartment boundaries. A basin modelling program has been developed, allowing calibration to known pressure and porosity data through an inversion methodology and the linking of multiple 1.5D forward models into a 3D framework that permits the description and analysis of the current pressure conditions within the model. An analysis of the main pressure compartments in the Eugene Island 330 Field area offshore northern Gulf of Mexico and in the Cassia Field area of the offshore Columbus basin, Trinidad, shows the use of the program for identifying the sealing portions of pressure compartment-bounding faults. An exploration strategy is outlined for the systematic identification and evaluation of pressure sealing fault traps.