A mathematical model of a quadrispherical electrostatic analyzer is formulated to give the response of such an instrument to a monoenergetic, unidirectional charged particle beam. The model is developed taking into account the aperture and collector geometry and it does not rely on the usual simplifying assumptions that the ratio of the analyzer plate separation to the mean radius is small or that any of the angular or energy acceptance windows are negligible. The model is compared to calibration data and is found to agree well. It is also readily adaptable to the determination of the response function of electrostatic analyzers with other patrial spherical geometries utilizing an arbitrary charged particle distribution input function.