Based on the atomic interaction potential with the embedded atom, molecular dynamics simulation was used to study the variation of Cu(001) surface caused by a Cu adatom and the hopping barriers of another Cu adatom in its vicinity. The results show that the Cu adatom may distort the positions of Cu atoms in the substrate to the extent of 2 lattice constants and the influence is as deep as 10 layers. Due to the interaction of the stress field between two adatoms, the hopping diffusion barriers of the adatoms are decreased and the adatoms are more active in diffusion than a single adatom. By comparing the difference of hopping barriers to and fro along the same diffusion path, the migrating behavior of the adatoms can be divided into two kinds of diffusion, depending on the distance between the two adatoms. If they are at a distance longer than the effective distance of the atomic interaction potentials, the diffusion of adatoms is affected only by the interaction of the stress field between two adatoms. If they are at a distance shorter than the effective distance of the atomic interaction potentials, the two adatoms should be considered as an ad-dimer in different states.