We propose two equivalent 1-D perturbation models for a fast fluidized bed considering compressibility effects. The first model is the explicit summation of incompressible and compressible terms. All compressible terms appear multiplied by the inverse squared gas sound propagation speed, s. In the second model, a lumped waving structure is presented, with just one term corresponding to each wave hierarchy. In both proposed models, the incompressible part was retrieved in the limit s > infinity. The Liu's linear stability analysis, based on Whitham's, was extended to estimate the compressibility contribution. Stability conditions on the propagation speeds and a criterion on the wave number were developed. This method was applied to two physical systems whose solid properties differ widely. It was shown that the effect of the fluid compressibility is at least as important as the effect of the solid compressibility modulus. (C) 2011 American Institute of Chemical Engineers AIChE J, 57: 2965-2976, 2011