Abstract: Since Orowan,Polanyi and Taylor defined the dislocation in crystal and analysed it by using elastic dynamics,dislocation has been deeply studied.Some models has been built.But that models are usually consecutive or halfdiscrete.Though they can resolve many problems about dislocation,they do not resolve the core of dislocation.Based on discrete model,the author only considers the affect of nearest atoms,using Green's function,calculates Peierls model of the dislocation in twodimensional square crystal latt...