This paper presents the results of a one-dimensional imbibition experiment in a dry Berea sandstone core, along with Computerized Tomography (CT) visualization of the saturation, and a new numerical model of the imbibition. The main aspects of the paper are: (1) a one-dimensional spontaneous imbibition experiment to measure the cumulative imbibition, permeability, and capillary pressure from the slope of saturation vs. square root of time curve; (II) a visual representation of the distribution of water saturation based on CT scan images; and (III) mathematical modeling and numerical simulations to compare with the experimental results.