A new procedure for obtaining saturation functions, i.e. capillary pressure and relative permeability, of tight core samples uses the pronounced end effect present in flooding experiments on such material. Commonly being a nuisance in core analysis, the end effect contains valuable information about the saturation functions. In core material with high capillary pressure, the end effect may allow determination of the saturation functions for a broad saturation interval. A complex core flooding scheme provides the fluid distributions and production data from which the saturation functions are computed by a least squares technique. An NMR technique is used for fluid distribution determination. The steady state situation at the end of a primary drainage experiment allows calculation of the drainage capillary pressure and the drainage relative oil permeability. The relative water permeability is calculated from the unsteady state data obtained during the transient part of this experiment. After a flow reversal, a new end effect develops at the opposite end of the core by an internal imbibition process, which at steady state allows calculation of the spontaneous imbibition capillary pressure and the imbibition relative oil permeability. Following a change from oil flooding to water flooding, the forced imbibition capillary pressure is calculated from transient pressure drop measurements. An undesirable interdependency of the saturation functions is avoided by their calculation from different data sets. Killough's method is employed to account for the scanning effect in hysteresis situations for both capillary pressure and relative permeability. The scanning parameter is determined as well. The procedure is demonstrated on chalk samples from the North Sea. The experimental time is intermediate between the centrifuge and porous plate methods. The procedure is superior to the centrifuge and mercury injection methods respectively by eliminating errors from end effects and using reservoir relevant fluids.