In this paper, we present a theoretical framework about correlated wave function for metal surfaces. The trial wave function for surfaces consists of a determinant of model single particle orbitals which are solutions of a variational potential with a consistent special symmetry, and a Feenberg-Jastrow pair correlation factor. In the "jel-lium model", we obtain expressions of ground state energy of metal surfaces. For the case without Feenberg-Jastrow factor in the wave function, we also obtain the expression for electron density distribution.