Modulated grid Faraday cup plasma analyzers are a very useful tool for makinginsitumeasurements of space plasmas. One of their great attributes is that their simplicity permits their angular response function to be calculated theoretically. In this paper we derive an expression for this response function by computing the trajectories of the charged particles inside the cup. We use the Voyager plasma science (PLS) experiment as a specific example. Two approximations to the ‘‘rigorous’’ response function useful for data analysis are discussed. The theoretical formulas were tested by multisensor analysis of solar wind data. The tests indicate that the formulas represent the true cup response function for all angles of incidence with a maximum error of only a few percent.