A numerical calculation of the steady flow in a laminar boundary layer on a fixed circular disk of finite size induced by some external axially symmetric motion is presented. The flow external to the boundary layer consists of a potential vortex which is coincident with the axis of the disk and an inward radial motion proportional to a power of the distance from the axis,r−m. Integration of the boundary layer equations is carried out starting at the edge of the disk and proceeding inward until a terminal solution is obtained. A numerical technique is employed which allows a solution to be obtained very near the center despite the extreme thickness of the boundary layer. A surprising result is the apparent lack of dependence of the terminal solution on either the conditions at the edge of the disk or the value ofmform<1. The limiting case when the spin vanishes is also calculated and the results support the view of Brown and Stewartson that algebraic decay can exist at a singular point in the boundary layer.