Pore pressure and fracture gradient are the two natural limits that exert the greatest influence on drilling costs and safety. Traditional empirical ''pore pressure'' models are limited to one lithology type (shale) and rely on incorporating petrophysical or drilling data vs. depth trend lines. We describe a new method that quantifies the effective-stress law, p = S - sigma(nu). This method uses petrophysical data (gamma ray, resistivity, density) and mineralogic stress/strain relationships to calculate pore pressure and fracture gradient, on a foot-by-foot basis, through all sedimentary rock types. Cretaceous marls and limestones have proven to be an obstacle for traditional pore-pressure evaluation methods. With numbers of high-pressure exploration wells in the North Sea Central graben increasing, there is a need for a better understanding of pressures through the Cretaceous and into the pressured formations below. This effective-stress-law method, which is used to determine pore pressure/fracture gradient, has been tested successfully in the complex limestone/shale and sandstone-shale sequences of the North Sea as an aid to well planning and real-time drilling operations decision making by use of measurement while drilling (MWD) petrophysical data. This method has recently been used successfully on two Central graben wells. BP drilled a high pressure/high temperature (HPHT) well in the second quarter of 1993 and used on-site pore pressure and fracture gradient (PP/FG) calculations, along with other more traditional pore-pressure methods, to help set an intermediate casing string at an optimum depth. We discuss results of these case studies and technical content of this pore-pressure method.