The main intent of the present study is to explore the varying fluid momentum and thermal energy characteristics of the laminar, steady, incompressible, two-dimensional, non-Newtonian pseudo plastic Williamson hybrid nanofluid over a stretching cylinder with variability in thermal conduction, suction, injection, heat generation and magneto hydrodynamic effects are considered. The mixture of Cu and MoS4 as nanoparticles in water as its base fluid is taken for this investigation as an hybrid nanofluid. The formulated governing PDEs are modified by employing with appropriate dimensionless transformations to get the non-linear ordinary differential equations. In accordance with the help of Runge-Kutta method of order four, shooting technique is implemented by making use of boundary value problem solver, bvp4c, which is accessible as an in-built function in MATLAB software for the numerical solution of the problem. The finding of this study are The values of Cf of the fluid grows with an increasing values of the physical parameters such as M and γ, whereas it is negatively influenced by λ. The values Nu of the Williamson hybrid Nano fluid has an increasing effect for the ascending entries of γ as well as Pr and has a reverse effect for the values of λ, M, β and ε of the fluid flow.