A special lattice resonance can be observed when the array period of a metal nanoparticle array matches the resonant wavelength of the localized plasmon resonance of an isolated particle. The lattice resonance is sharper and its linewidth is narrower than the localized plasmonics resonance of a single particle. According to the modified long wavelength approximation approach, we discuss the extinction cross-section of the rectangular array in terms of the array factor and the particle polarizability. In this paper we emphasize the polarization characteristics of the regular array when the laser is incident vertically under different polarizations, and we also discuss in detail the variation of the array factor with the direction of electric dipole, and its influence on extinction cross section of the particle array. The square lattice with big size is polarization independent, while the rectangular lattice is polarization dependent. The coupling between the neighboring particle dipoles along the two lattice vectors of the regular array gives rise to a maximum value of its array factor, which determines a minimum value of the extinction cross section. When the incident light is polarized along one of the lattice vectors, the dipole coupling along that direction can be ignored since the particles are located in the far field of its neighboring particles, and the relevant peak in the array factor disappears.