A numerical algorithm is presented for computing the laminar two-dimensional flow of a second grade fluid near a stagnation point when the fluid is extracted from the plane at a uniform rate. The algorithm is applicable for all values of the physical parameters of the problem. Also the asymptotic solutions valid for large values of the suction parameter are derived and the results obtained from them compared with the exact numerical solution.Finally, the flow of a second grade fluid past a stretching sheet with suction is considered. This problem has an exact solution and it is used as a benchmark for testing the numerical algorithm presented here.