Square hollow nanostructure can induce a large-area enhanced electric field at the main plasmon peak. Therefore, it can be used as a substrate for the surface enhanced Raman scattering. The effects of the incident polarization on the extinction spectrum and the electric field distribution of the square Ag nanostructure are studied by the discrete dipole approximation method. The results show that the plasmon peaks do not shift with the variation of incident polarization. However, the electric field distribution is strongly dependent on the direction of incident polarization. Additionally, the effect of the electric field coupling between adjacent square Ag nanostructures on the plasmon mode is also studied. It is found that the plasmon resonance can be tuned by varying the separation between adjacent squares. These results could be used to guide the preparation of such closed nanostructures for specific plasmonic applications.