Dynamic displacement experiments and numerical two-phase flow estimation program are presented in this study. Unsteady-state core-flooding system was designed and utilized for oil-water dynamic displacement experiment. Two in situ sandstone core plug samples were used to investigate relative permeability via diesel and 3 wt % brine as non-wetting and wetting phase fluids. The transient data (pressure drop and produced fluid volume) were collected automatically for oil-water relative permeability computation. For relative permeability analysis, an inverse method program was constructed with four components: (a) an IMPE finite-difference numerical simulator of the flow through the core; (b) functional Corytype power law model of relative permeability in terms of a set of adjustable parameters found by minimizing an objective function; (c) the objective function formed by the sum of the square of the differences between the observations and calculated data; (4) the Gauss-Newton with Levenberg-Marquardt modification procedure for the leastsquares problem to minimize the objective function definition. All the above processes are embodied in relativepermeability calculation program, RCP, which is constructed in this study using FORTRAN language.