The axisymmetric stagnation flows towards a shrinking sheet of Newtonian fluids has been solved numerically by using SOR Iterative Procedure. The similarity transformations have been used to reduce the highly nonlinear partial differential equations to ordinary differential equations. The results have been calculated on three different grid sizes to check the accuracy of the results. The problem relates to the axisymmetric stagnation flows towards a shrinking sheet when α < 0 and if α > 0 the axisymmetric stagnation flows towards a stretching sheet. The numerical results for Newtonian fluids are found in good agreement with those obtained previously.