We performed non-local electrical measurements of a series of Py/Cu lateral spin valve devices with different Cu thicknesses. We show that both the spin diffusion length of Cu and the apparent spin polarization of Py increase with Cu thickness. By fitting the results to a modified spin-diffusion model, we show that the spin diffusion length of Cu is dominated by spin-flip scattering at the surface. In addition, the dependence of spin polarization of Py on Cu thickness is due to a strong spin-flip scattering at the Py/Cu interface.