Abstract: The flow of Rivlin-Ericksen fluid past a porous vertical wall with the constant suction under the influence of uniform transverse magnetic field is studied. The velocity distribution, temperature distribution, rate of heat transfer, and the coefficient of skin friction are analyzed under the initial and boundary conditions. The effects of magnetic field, visco-elastic parameter, Prandtl number and suction parameter have been investigated on the flow of Rivlin-Ericksen fluid and the results are computed graphically for different values of the parameters.