The optical properties of nanoparticles and their array are closely related to their surface plasmon resonance of the particle and periodic structure parameters. In this paper, optical response features of single Ag nanosphere and periodical two-dimensional structure arrays are theoretically studied. The Mie theories and the multipole resonance theory are employed in the simulation. For Ag spheres each with a radius of less than 40 nm, one extinction peak can be observed and attributed to electric dipole resonance. When the radius of Ag sphere is more than 40 nm, apart from the peak contributed by the electric dipole, there is a peak of extinction at short wavelength, caused by resonance of the electric quadrupole. Generally, the frequency of multipole resonance decreases with increasing particle radius. The simulated results are in accord with the experimental data. For an infinite two-dimensional Ag-nanosphere arrays, two resonance peaks come from the dipole resonance of single particle and the Wood-Rayleigh anomalous diffraction. The frequency of multipole resonance can be controlled by tuning the size and the periodicity distribution of arrays. This paper provides a significant method to design advanced nanostructures with particular optical properties.