The extended core structure of the dissociated edge dislocation in Al,Au,Ag,Cu and Ni is determined within lattice theory of dislocation.The 2D dislocation equation governing the displacements is coupled by the restoring forces that are determined by the parameterization of the generalized stacking fault energies.The Ritz variational method is presented to solve the dislocation equation and the trial solution is constituted by two arctan-type functions with two undetermined parameters.The core widths of partial dislocations are wider than that obtained in generalized Peierls-Nabarro model due to the consideration of discreteness of crystal.