AbstractIn this study, the optimal homotopy analysis (OHAM) technique has been examined to solve the laminar magnetohydrodynamic flow (MHD flow) on the upper‐convected Maxwell fluid on an isothermal porous stretch surface. A study on the effects of parameters like the relaxation time, suction/injection velocity, as well as the magnetic number on velocity over a sheet was conducted and these results are compared to the corresponding previously available results. It was observed that the thickness of the boundary layer is lowered by enhancing , , and values. Opposing this, it was observed that large values increase the magnituIIde. It is found that OHAM is an efficient method capable of giving a greater degree of accuracy in numerical values of flow parameters even after fewer approximations.