The two-Γ€imensional steady flow of an incompressible elastico-viscous fluid through a porous channel that has the fluid sucked or injected with different normal velocities V1 and V2 at the walls is considered. For the viscous case Terrill and Shrestha [2] have given a series solution for small suctioI1 Reynolds number. In this paper the solution of [2] is extended to include the effect of the elasticity of the fluid. It is found that the elasticity of the fluid comes into effect only when suction or blowing is present. The general expressions for the pressure distribution and the friction coefficient are given and are found to increase as the elastic parameter increases. Finally, the resulting solution is confirmed by numerical results. Nomenclature p,g stress tensor p arbitrary isotropic pressure g~Β» metric tensor of a fixed coordinate system x t T *~ stress components, defined in (2) ~fj" rate of stress tensor, defined in (8) d ~~ rate of strain tensor N(T) distribution function of relaxation times T co 70 = S N(T) dr limiting viscosity at small rate of shear 0 oo k0 ~ ~ TN(T) dr short lnemory coefficient 0 density components of velocity vector components of the velocity gradient tensor kinematic viscosity