This paper presents a general three-dimensional Stokesian Dynamics model that dynamically simulates the motion and deposition of particles as they approach and migrate through a porous medium. The model allows for variations in the fluid velocity, particle size, and forces or torques acting on the particles. The use of a Stokesian dynamics approach provides a unified framework in which no a priori assumptions about the type of filtration need be made. The model is valid for the hydrosol filtration of dilute suspensions. One of the most important and perhaps least understood issues in filtration is the effect of previously deposited particles on the subsequent deposition of particles. As each particle deposits on a grain, it alters the fluid flow field. This distortion in the fluid flow can significantly affect the motion of subsequent particles. The fluid flow field and the particle trajectory therefore dynamically evolve with time and depend on the size and location of the collector grains as well as the deposited particles. The effect of particles lodging in pore throats to cause plugging is twofold. First, particle plugging will change the fluid flow field around the grains that are adjacent to the plugged pore throat. Furthermore, as particles are diverted away from the blocked pore throats, the concentration of particles passing through the open pore throats will increase. This in turn may lead to a rapid buildup of particles on these adjacent collectors until they are also clogged. Consequently if the conditions of deposition are such as to encourage extensive particle bridging, this will eventually lead to a situation where particle bridging occurs across all the pore throats. If this occurs, or near, the face of the filter bed, the particles will tend to deposit on each other and the mode of filtration will change from deep bed filtration to “cake” formation. The model presented in this paper allows us for the first time to dynamically simulate this process of particle deposition, bridging, and cake formation.