In the present investigation we have studied the peristaltic flow of a Carreau fluid in a rectangular duct. The flow is investigated in the wave frame of reference moving with the velocity $c$ away from the fixed frame. The peristaltic wave propagating on the horizontal side walls of a rectangular duct is studied under long wave length and low Reynolds number approximation. The analytical solutions of velocity and pressure gradient have been found under lubrication approach with the help of Homotopy perturbation method. Graphical results are displayed to see the behavior of various emerging parameters of Carreau fluid. The comparison of the present work is also made with the existing literature.