A computationally efficient and fast method for characterizing MHD fluid flow based on the “core flow” approximation is presented. The results of analysis of a number of practical problems that were solved using this method are also discussed. At very high Hartmann number and interaction parameter and at very small magnetic Reynolds number, the equations describing the flow are essentially linear and are therefore solved more easily. By solving these equations, the three-dimensional characteristics of the flow can be examined using a two-dimensional computer code. The method used to solve these equations is an iterative one. A velocity profile is assumed and the equations are solved in a plane in the fluid. The equations are then solved in the domain of the duct wall. The potential in the wall is compared to the potential in the fluid along the magnetic field lines. If the variation of the potential along field lines is not correct, the velocities are adjusted. The potential distribution in the fluid can then be calculated again. This procedure is repeated until the variation of the potential along field Unes is correct.This method is applied to flow in a conducting duct with a transverse magnetic field that varies in the flow direction. The pressure drop dependence on various factors is discussed. The method appears to be particularly suited to problems with complex geometries, because the equations may not be as complicated as in the direct integration method. The results of the analysis are shown to compare well with experimental results.