The method of characteristics is applied to the nonlinear equations describing two phase flow. The method shows how a small disturbance changes with time and distance and can, eventually, produce a flow discontinuity similar to a shock wave in gases. The parameters entering the analysis are the amplitude of the initial disturbance, the wave length of the original disturbance, the particulate pressure function, the particulate size, the uniform fluidization voidage, the uniform fluidization velocity, the fluid viscosity, the particulate density, and the fluid density. A study of the parameters indicates a qualitative agreement with experimental data for gas-particulate fluidized beds. It is shown theoretically, and these results have been confirmed experimentally, that the following factors increase bed stability: a decrease in the particulate size, an increase in the bed density, an increase in the fluid viscosity, and a decrease in the particulate density. This theory is the first to show rigorously that a small disturbance can lead to a particulate shock wave which may indicate the creation of a bubble. 18 figs, 2 tables. (RWR)