An analysis is made on a steady flow of an incompressible visco-elastic fluid (of small memory) past a porous plate subject to uniform suction or blowing. The fluid and the plate rotate in unison with uniform angular velocity about an axis perpendicular to the plate. It is shown that for a visco-elastic fluid of small memory, a boundary layer is formed for uniform suction or blowing at the plate. It is found that the primary velocity increases whereas the secondary velocity increases near the plate and decreases away from the plate with an increase in the elastic parameter. The secondary flow shows flow reversal for a large elastic parameter. It is found that both primary and secondary velocities increase near the plate and decrease away from the plate with an increase in the rotation parameter. It is also found that the shear stress due to primary flow increases with an increase in either the elastic parameter or rotation parameter. On the other hand, the shear stress due to secondary flow decreases with an increase in the elastic parameter while it increases with an increase in the rotation parameter. The temperature distribution in the boundary layer is also determined. It is shown that elasticity leads to an increase in heat transfer at the plate.