We construct a nonlinear lattice model to investigate the dynamics of nonlinear behavior in phononic crystals (PnCs). Two types of mass points and springs are introduced in the model to reproduce the difference in material properties between the scatterers and background in PnCs. The nonlinearity is introduced to the model by changing the mass of each mass point depending on the displacement gradient at the mass point. We numerically confirm that both the 1D and 2D models have the bandgap in the linear dispersion relation. Moreover, in both model, switching behavior of wave propagation is found.