Abstract: An analysis is made of the flow of an incompressible viscoelastic fluid (of small memory) over a porous plate subject to suction or blowing. It is found that velocity at a point increases with increase in the elasticity in the fluid. It is also shown that wall shear stress depends only on suction and is also independent of the material of fluids. No steady solution for velocity distribution exists when there is blowing at the plate. Temperature distribution in the boundary layer is determined and it is found that temperature at a point decreases with increase in the elasticity in the fluid.