Effects of displacement pressure, pressure gradient, and flow rate on the shape of relative permeability curves have long been a controversial subject in petroleum literature. For drainage experiments it has been reported that the relative permeabilities are independent of flow rate. However for imbibition experiments the rare literature, mainly concerned with oil-water phases, does not agree on this point. Three-phase, unsteady state CT scanned displacement tests were conducted using fired Berea sandstone to obtain relative permeability and capillary pressure data. Eight percent Potassium Bromide eloped brine hexane, and nitrogen gas was used. Relative permeabilities and capillary pressures were then estimated simultaneously after minimizing a least squares objective function containing all available and reliable experimental data obtained from three phase imbibition experiments using an automated history matching code where simulated annealing was utilized. It has been found that brine and hexane relative permeability curves were affected much more compared to the gas relative permeability curve, especially near the endpoints. Moreover gas relative permeabilities decreased,vith increase inflow rate. Capillary pressure curves were affected in a similar manner. Finally, in order to confirm the above results an approach consisting of matching, at the same time, the fastest, the slowest, and a medium rate experimental data were tested. The algorithm failed to find a set of flow function curves which could fit both experimental data; therefore the conclusion was that for three-phase imbibition the flow functions depend on the flow rate.