The initial-boundary value problem representing the supersonic flow of a viscous or inviscid gas is solved by a forward marching procedure which integrates a set of coupled nonlinear multidimensional equations. The numerical method is based upon an alternating-direction implicit scheme and sample calculations have been performed to demonstrate the capabilities of the procedure. The specific problem considered concerns the supersonic flow of a three-dimensional jet exhausting into a supersonic ambient stream. It is shown that stable and apparently accurate solutions can be obtained for axial steps considerably larger than those normally permissible with many conditionally stable procedures. The computational cost per grid point per axial step in the present problem was very approximately only a factor of 2 greater than that required with the conditionally stable methods.