In this computational study, the tribological characteristics of the flow of a visco-plastic fluid around a pair of cylinders in a channel are thoroughly analyzed. To numerically solve the governing equations, this investigation makes use of the Galerkin's Finite Element Method (FEM) in conjunction with Newton's and PARDISO solvers. The stable finite element pair (P2/P1) has been selected for the space discretization purpose. The impacts of several physically important parameters on the flow characteristics are investigated in depth, including the spacing ratio (GP), the power law index (n), the Bingham number (Bn), and the Reynolds number (Re). When using different gap spacing ratios (GP), the drag coefficient (CD) and lift coefficient CL were found to be strongly dependent on GP. The pressure, velocity, and viscosity profiles are plotted for varying n and Bn. In addition, the velocity behavior is observed along y-direction in a channel through line graphs. Code validation is done as special case when Bn=0andn=1. It has been observed that the gap between the obstacles can influence the overall flow pattern and subsequently the drag and lift forces.