When liquid suspensions containing fine solids are treated in packed-bed bubble reactors, bed plugging develops and increases the resistance to two-phase flow. Accumulation of fines in the catalyst bed increases the reactor pressure gradient until eventually the unit must be shut down and the physically deactivated catalyst replaced. Currently, physical models linking the two-phase flow to the space-time evolution of fines buildup are virtually nonexistent. An attempt has been made with this contribution to fill in this gap by developing a unidirectional dynamic multiphase flow model based on the volume-average equations of mass and momentum balance for the gas and suspension and the species balance for the fines. Coherent with experimental observations, the model hypothesizes that plugging develops through deep-bed filtration mechanisms. The model incorporates physical effects of porosity and effective specific surface area changes due to the fines capture by the collecting catalyst particles, inertial effects in the gas and suspension, and coupling effects between the filtration parameters and the interfacial momentum exchange force terms. For the rationalization of deep-bed filtration phenomena in packed-bed bubble reactors, parametric studies of the effects of liquid velocity and viscosity, gas density and velocity, fines concentration in the influent suspension, and fines diameter on the plugging dynamics are discussed.