Counter-current imbibition occurs when brine spontaneously displaces oil from a very strongly water-wet rock. Experiments are usually carried out on cylindrical core plugs which have all of their faces open, mainly because this is easiest to do and also because it appears to give the most reproducible results. The flow patterns are complex, but a reasonable approximation can be obtained by assuming piston-like advance of fronts from the radial outer face and both flat ends. This separates the flow pattern into two types: linear imbibition into cones and radial imbibition into the surrounding toroid ring. Production versus time curves have been calculated for cylinders of varying aspect ratios and other core shapes. The analytical results confirm the experimental observation that sample shape does not have much effect on the shape of the production versus time curves. Bearing in mind the inherent variability of experimental results for individual core samples, the differences would be difficult to detect in experiments. The time for imbibition to be completed scales as the characteristic length. The function given by Ma et al. (J Pet Sci Eng 18: 165-178, 1997) requires only a small correction factor for agreement with the analytical result. The present analysis makes straightforward the comparison of results from the complex flow condition of all-faces-open imbibition with results from linear and radial experiments. A comparison is made with published results.