A pseudo-similarity solution is obtained for the flow of an incompressible fluid of second grade past a wedge with suction or blowing at the surface. The non-linear differential equation is solved using quasi-linearization and orthonormalization. The numerical method developed for this purpose enables computation of the flow characteristics for any value of the parameters K, a, and b, where K is the dimensionless normal stress modulus of the fluid, a is related to the wedge angle, and b is the suction or blowing parameter. A significant effect of suction or blowing on the wall shear stress is observed. The present results match exactly with those from an earlier perturbation analysis for Kx2a ≤ 0.01 but differ significantly as Kx2a increases.