Over the last century lots of efforts have been put in the reduction of profile drag. Boundary layer suction is one of the effective methods to achieve this goal. A laminar boundary layer will be stabilized preventing transition from laminar boundary layer to a turbulent one and yielding larger areas of laminar flow, which generates less drag. In this thesis, mathematical models for incompressible laminar steady flows of three different non-Newtonian models with/without magnetohydrodynamic effect are developed. It is analyzed theoretically and found that much improvement can be achieved by implementing boundary layer suction. Moreover, slip at wall/presence of magnetic field applied normal to main flow velocity further reduces the drag.