The Present Paper Provides the Non-Newtonian Fluid Flow Between Two Fixed Parallel Horizontal Plates. a Mathematical Model Is Developed to Describe the Fluid Motion. the Fluid Is Assumed to Depend Exponentially on Viscosity. the Governing Equations Are Non-Dimensionalized and the Steady State Equations Are Solved Numerically Using Shooting Method Technique. the Effect of the Nature of the Non-Constant Viscosity of a Function of the Space Variable Y Shows Much Influence on the Velocity Fields.