A Stabilized Form Of Finite Element Formulation Known As The Galerkin Least-Squares (Gls) Method Is Implemented Here For Solving The Two-Dimensional Incompressible Non-Newtonian Fluid Model Of Blood Flow In A Diseased Artery. The Modelling For This Type Of Flow Is Based On The Conservation Of Mass And Momentum Equations, Coupled With The Generalised Newtonian Liquid (Gnl) Constitutive Equation Characterized By The Generalised Power Law (Gpl) Model. The Flow Of Blood In This Present Study Are Assumed As Steady, Laminar And Fully Developed. The Finite Element Algorithms Considered Herein Are First Solved For The Newtonian Fluid In A Straight Artery With A Bell Shaped Stenosis For Validation Purposes. As The Efficiency And Validity Of The Proposed Algorithms Are Obtained Through Comparison With The Findings From Existing Literature And Comsol Multiphysics 5.2 Software. Then, The Algorithms Are Being Implemented To The Generalised Power Law Fluid Model Of Blood Flow In A Bifurcated Artery With Overlapping Stenosis Located At The Parent's Arterial Lumen. The Numerical Results Illustrate The Arising Of Distinct Sizes Of Vortex Shedding Downstream Of The Stenotic Region For Each Generalised Power Law Index