A numerical study has been conducted to investigate the steady forced convection stagnation point-flow and mass transfer past a permeable stretching/shrinking sheet placed in a copper (Cu)- water based nanofluid. The system of partial differential equations is transformed, using appropriate transformations, into two ordinary differential equations, which are solved numerically using bvp4c function from Matlab. The results are obtained for the reduced skin-friction and reduced Sherwood number as well as for the velocity and concentration profiles for some values of the governing parameters. These results indicate that dual solutions exist for the shrinking sheet case (λ < 0). It is shown that for a regular fluid (f = 0) a very good agreement exists between the present numerical results and those reported in the open literature.