This study employs a two-dimensional and incompressible flow of Herschel–Bulkley visco-plastic materials in order to investigate the hydrodynamic forces that are acting on a barrier that is located close to the inlet of a channel. As the benchmark configuration, the flow domain that has been selected is a channel that still contains the impediment. The two important parameters of the Herschel–Bulkley Model (HBM) are the yield stress τy and power law index n. Obtaining special situations within the HBM, such as Newtonian, power-law, and Bingham fluids, can be accomplished by assigning certain values to these parameters at the appropriate times. Utilizing a numerical strategy grounded in the Finite Element Method (FEM), we tackle the nonlinearity of the governing equations as well as the viscosity models. As a result of this nonlinearity, FEM becomes an essential tool. The generation of a refined hybrid mesh is done in order to guarantee accuracy in the computations. The stable finite element pair (ℙ2∕ℙ1) has been selected for discretization purposes. The discretized nonlinear system is linearized with Newton’s method and subsequently, a direct linear solver PARDISO has been employed in the inner iterations. The pressure, velocity, and viscosity profiles are plotted for various values of n and Bingham number (Bn). In addition, the velocity behavior is observed along the y-direction in a channel through line graphs. Code validation is done as a special case Bn=0 and a good agreement is found with the results available in the literature. Finally, a correlation analysis has been performed for the drag coefficient Cd and lift coefficient Cl.