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We study here the effectiveness of the optimal homotopy asymptotic method (OHAM) in solving non-linear differential equations of non-Newtonian fluids. To this consequence, we consider the Oldroyd 6-constant fluid when it demonstrates slippage between the plate and fluid generating non-linear boundary value problems. The problems of plane Couette flow, generalized Couette flow, and plane Poiseuille flow are considered. Graphs of the results are plotted to show the performance of the method in terms of velocity profile. It is observed that the method is quite easy to implement, having latent potential to handle such kinds of non-linear problems and yield accurate results at minimum to low computational work.