An equivalent-circuit model is an effective tool for the analysis and design of metamaterials. This paper describes a systematic and theoretical method for the circuit modeling of meta-atoms. We focus on the structures of wired metallic spheres and propose a method for deriving a sophisticated equivalent circuit that has the same topology as the wires using the partial element equivalent circuit (PEEC) method. Our model contains the effect of external electromagnetic coupling: excitation by an external field modeled by voltage sources and radiation modeled by the radiation resistances for each mode. The equivalent-circuit model provides the characteristics of meta-atoms such as the resonant frequencies and the resonant modes induced by the current distribution in the wires by an external excitation. Although the model is obtained by a very coarse discretization, it provides a good agreement with an electromagnetic simulation.