Steady state equations are written for a one dimensional moving granular bed filter. These equations contain three terms that must be related to the operating conditions such as gas velocity, grain size, particle size, local loading of suspended and captured dust, etc. The three terms are J, the rate of particle deposition onto a single grain including the adhering dust particles, F, the drag force on a single grain including its adhering dust particles, and R, the rate of re-entrainment of previously captured dust from a single grain. Methods of estimating J and F are briefly reviewed; at present we are unable to estimate R and take this rate to be proportional to the concentration of captured dust. Solutions to the equations are given for a mono disperse size dust. The solutions show the favorable influence of dust deposit on particle capture rate and the negative influence of re-entrainment which becomes “catastrophic” if the re-entrainment becomes too large. Predictions of the model are compared with Combustion Power Company’s cold flow filter tests. The model underestimates the observed pressure drop, but this is probably largely due to added pressure losses at the inlet to the filter and to the non-one dimensional nature of the real filter, factors not taken into account in the calculations. The predicted penetrations for particles 1.56 um in diameter are compared with the measured penetrations of particles in the 1 to 2 um size range in a manner found useful by Combustion Power Company for correlating overall penetration. The theoretical predictions are found to reproduce the trends and to be semi quantitative if reasonable values of the re=entrainment rate are adopted.