Relative permeability and capillary pressure are the primary flow parameters required to model multiphase flow in porous media. Frequently, these properties are estimated on the basis of unsteady state laboratory displacement experiments. Interpretation of the flood process to obtain relative permeability data is performed by application of frontal advance theory. Application of frontal advance theory has a number of limitations. Therefore, the flow rate of injection water to the core must be sufficiently large that capillary effects, particularly at the outlet end of the core, which is called capillary end-effect, are negligible. In some cases, capillary end effects in core flood experiments can significantly influence relative permeabilities and final saturation levels. An automatic numerical method with a parameter estimation technique is proposed for simultaneous determination of relative permeabilities and capillary pressure from the results of a two-phase flow modeling, including capillary end-effect in outlet boundary. In this study, an interpretation method using genetic algorithms to minimize adjustable parameters is suggested. The advantage and convenience of a genetic algorithm is that the method converges in all situations to a global optimum.