Surface lattice resonances due to regular periodic array of metallic nanoparticles can be attributed to the mutual coupling between the localized surface plasmon resonances of different nanoparticles. A comparison of resonant effect between the single particle and the array shows that the resonance line width can be significantly reduced. In this paper, we extend the coupled dipole approximation to solving the electromagnetic characteristics of the particle ring structures with rotational symmetry, and propose an analytical model for the double ring array of metallic nano-particles. Furthermore, we derive the general resonant condition of the double ring array and investigate some concrete cases in detail. It shows that the full resonance of the whole array depends crucially on the structural parameters, whose enhancement factor can be extremely high. But a slight change in the structural parameter willlead the enhancement factor to decrease sharply. We also find that the radiation field of the full resonance effect will be independent of the external field, which provides us a simple approach to producing a localized optical field with complex space distribution. This proposed structure can possess potential applications in various fields such as metasurface, optoelectronics, optical manipulation, communication, and biosensing.