Suspension-feeding ciliates, either bacteriovorous or planktonic, are adapted to feed on particulate food matter of size much smaller than their own size. These microorganisms collect their prey by generating water currents that draw prey toward their capture surfaces. Under such conditions food particles are treated in bulk, and captures of individual food particles from a suspension by individual single-celled organisms are discrete events that occur at random intervals of time. Each such event is followed by a sequence of additional events that also occur at random intervals of time. This sequence culminates in the incorporation of the digestible portion of the food particle into the cell's cytoplasm and the expulsion of the indigestible portion from the cell. In theory, the rate of the overall ingestion-digestion process can be limited by the passage of particles through any stage of this sequence of events. In this paper, we assume that only the initial events in the sequence, those that occur in the oral region of the cell, limit the rate of the ingestion-digestion process, and we develop a discrete, stochastic model of filter feeding based on that assumption. We use the model to show how advanced instrumentation, such as flow cytometry, can be used to measure parameters of the model and also to answer a number of important questions about the mechanism of filter feeding. We show also how the model can be applied to nonhomogeneous cell populations for which parameters of the model are distributed.