Employing the density-functional theory within the generalized gradientapproximation, we investigate the interaction between atomic Si andthe Cu(100) and (111) surfaces. Various structures of on-surfaceadsorption as well as surface-substitutional adsorption for a widerange of Si coverage are considered. Our results show that both Cu(100)and (111) surfaces are active for adsorption of Si. The c(2×2)-Si/Cu(100) surface alloy is energetically favourable for a largerange of Si chemical potential while c(2×2)-Si/Cu(111) isenergetically favourable only under Si rich conditions.