Anaerobic packed bed processes are used to treat industrial wastes containing high concentrations of readily biodegradable organics. Dynamic mathematical models for anaerobic up-flow and down-flow packed bed processes have been developed and verified semi-quantitatively by using experimental data and information from the literature. The dynamic models are then used to study the dynamics, stability and control of the process. The biological kinetic models involve four different groups of bacteria: acid producing bacteria (X\sbG), hydrogen utilizing methanogens (X\sbH), acetoclastic methanogens (X\sbA) and propionic acid utilizing acetogens (X\sbP). The effect of hydrogen on the acid formation stage and propionic acid degradation has been incorporated in the models using complementary Monod type equations. Modified inhibition functions are proposed for the growth rates of X\sbA and X\sbP. In these functions, high concentrations of total unionized volatile fatty acids and unionized propionic acid are assumed to be toxic to X\sbA and X\sbP, respectively. The hydraulic model of the up-flow anaerobic packed bed process is represented by a slurry reactor followed by a fixed film reactor approximated by complete mixing tanks in series. A constant thickness of biofilm and uniform bioactivity are assumed for the down-flow anaerobic packed bed process. A single complete mixing tank with dead space, short circuiting, and complete mixing tanks in series is used for approximating the hydraulics of down-flow process with and without recirculation, respectively. Semi-quantitative agreement between simulation results using the proposed models and data obtained from experiments and the literature was obtained. High resistance to hydraulic overloading and rapid recovery after shock loadings was demonstrated for the anaerobic packed bed processes. The model suggests that the more intense the overload, the greater the accumulation of propionic acid. System failure due to organic loadings could be predicted by incorporating modified inhibition functions into the overall model. The concentrations of hydrogen and propionic acid can be good stability indicators. On-off control of the recycle flow rate using hydrogen and propionic acid concentrations as the measured variable was simulated. This control strategy can prevent process failure for pulses of short duration and delay process failure for step changes. The time delay obtained by this control can provide operators the time needed to take other corrective actions.