In this researcha new approach has been developed to calculate the effective mass density for a composite containing local resonance units consisting of a hard sphere corea soft shell layer surroundingand a stiff host medium. The composite has been developed as low-frequency sound shielding material. Different from the model in the original paper based on wave propagation theorythe new approach is based on vibration theory. The natural frequency of local resonance unit is calculatedand then the composite behavior under harmonic load is investigated. It is shown that the effective mass density of the composite can turn to negative and infinitely close to the local resonance. In order to examine the influence of important parameters on the resonant frequency and effective mass densitya parametric study has been carried out. It is found that a thicker soft layer with smaller modules can lead to lower resonant frequency. The predictions of wave spectral gap from the new approach and from the model in the literature are almost identical. © 2011 ASCE.