The magnetohydrodynamic (MHD) flow of an electrically conducting fluid is considered in a long channel (pipe) of rectangular cross-section in which the fluid is driven by a pressure gradient and the flow is steady, laminar, fully -developed. The flow is influenced by an external uniform magnetic field applied perpendicular to the channel-axis. Thus, the velocity field (V) over right arrow = (0, 0, V) and the magnetic field (B) triple over dot = (0, B-0, B) have only channel-axis components V and B on the cross-section of the channel which is a rectangular duct. The finite difference method (FDM) is used for solving the governing equations with the boundary conditions which include both the slipping and variably conducting side walls. The well-known characteristics of the MHD flow including the slipping velocity are observed. Thus, the FDM enables one to depict the effects of Hartmann number, conductivity and slip parameters on the behavior of both the velocity of the fluid and the induced magnetic field at a small expense.