A laminar wake model is studied which assumes that the boundary layer equations are valid in a shear layer on the axis of symmetry, and that the local pressure is determined by a displacement interaction with the inviscid outer flow. The finite difference method used places no restrictions on the shape of the velocity profile. The qualitative features of the solution are the same as those found by previous investigators using integral methods, in that an otherwise arbitrary initial condition (the local free stream Mach number) is determined by the fact that only a particular value results in a physically meaningful solution. Two methods of finding the particular solution are investigated. (Author).