Mathematical models for pulsed fluidization are systematically discussed. Several undetermined constitutive relationships are included in the General Two-Fluid Model (GTFM), the adjustable parameters of which are always chosen at will to some extent. Although there are no adjustable parameters in the Basic Two-Fluid Model (BTFM), its eigenvalues are complex numbers and it is ill-posed for initial-value problems. The Local Equilibrium Model (LEM), a further simplification of BTFM, is discussed at length. Although the model is very simple, it is highly capable of simulating complex processes in pulsed fluidization over a broad range of operating parameters, and its numerical results well fit experimental results in both the variation of bed height and the distribution of particle concentration as fluidizing velocity varies.