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The numerical analysis of continuous boundary-layer suction on a flat plate at zero angle of attack is the focus of this study. A uniform flow is prescribed upstream of the plate. The governing equations, the Navier-Stokes and continuity equations are presented by the vorticity-stream function formulation. A transformation is made from the physical to the computational domain and the resulting equations are solved numerically by the ADI and SOR methods, respectively. Reynolds numbers from 103 to 104 are considered. A second-order upwinding scheme is employed to numerically stabilize the solution. A comparison is made between flows with and without suction. Preliminary results are presented for the solution behavior as a function of such parameters as Reynolds number, grid resolution and numerical representation of the boundary conditions.