The focus of this research is to observe how suction/injection affects the stagnation point flow and heat transfer in a hybrid nanofluid over stretching/shrinking cylinder. Silver (Ag) and copper oxide (CuO) nanoparticles are dispersed in pure water to create a hybrid nanofluid. By using similarity transformations, the governing partial differential equations are turned into a ordinary differential equations which are then solved by implementing bvp4c function in MATLAB software. The influence of the nanoparticle volume fraction, magnetic parameter, curvature parameter and suction/injection parameter, on velocity and temperature profiles, local skin friction and local Nusselt number are discussed and presented in graphical forms. The results indicate that all of the problems have dual solutions for a given range of parameters. It is noticed that with the suction effect, energy losses is reduced, thus the heat transfer increases and decreases the boundary layer separation. Furthermore, the presence of curvature parameter and suction effect expand the range of dual solutions. In addition, the rate of heat transfer for hybrid nanofluid was higher than viscous fluid and nanofluid.