Abstract: Applying the optimal homotopy asymptotic method (OHAM) to study three nonlinear problems,plane Couette flow,plane Poiseuille flow and plane Couette-Poiseuille flow,of the Oldroyd 6-constant fluid.Firstly,the governing equation and boundary condition of plane Couette flow,plane Poiseuille flow and plane Couette-Poiseuille flow in the Oldroyd 6-constant fluid were introduced respectively.Then applying the optimal homotopy asymptotic method was used to solve the problem,and carrying out some simulations.Finally,the effect of the slip parameter on the velocity profile was discussed based on the simulations.