Abstract Four water/oil and four oil/air linear counter-current spontaneous imbibition experiments were performed on Berea sandstone cores with permeabilities ranging from 0.065 to 1.094 μm 2 . The cores were initially 100% saturated with non-wetting phase and all faces except one end were sealed. The experiments showed a clear frontal displacement mechanism. Capillary pressure was the driving force of the imbibition process. As well as viscous drag in both phases between the imbibition front and the open face, there is a significant opposing capillary back pressure associated with production of non-wetting phase at the open face. The location of the imbibition front, the overall changes in core saturation, and the pressure in the nonwetting phase in the dead end space ahead of the imbibition front, were monitored during the course of imbibition. The dead end pressure was essentially constant after a short start-up period. The distance advanced by the imbibition front was proportional to the square root of time. Based on the assumption that the properties of Berea sandstone of different permeabilities can be scaled, the experimental data were matched by numerical simulation to predict the saturation and pressure profiles, the saturation and capillary pressure at the imbibition front, and the capillary back pressure at the open face. The ratio of the capillary back pressure to the estimated capillary pressure at the imbibition front ranged from approximately 1/3 to 2/5, for oil displacing air, to approximately 1/9 to 1/4, for water displacing oil.