We propose a multi-displacement continuum (MDC) model to characterize the local resonance presented in a lattice system. Dispersion curves in a mass-in-mass system are studied and compared to the single-displacement model. It is shown that the dispersive relations and the local resonant band gap structures can be adequately described. The acoustic mode can be accurately predicted, while the optical mode is correctly predicted for certain frequency range, where the wave length is large enough. The single-displacement model fails to describe the bang gap structure inherent in the system due to local resonance. We propose a multi-displacement continuum (MDC) model to characterize the local resonance presented in a lattice system. Dispersion curves in a mass-in-mass system are studied and compared to the single-displacement model. It shows shown that the dispersive relations and the local resonant band gap structures can be precisely characterized that while the optical mode is correctly predicted for certain frequency range, where the wave length is large enough. The single-displacement model fails to describe the bang gap structure inherent in the system due to local resonance.