The human visual system obeys Listing's law, which means that the cyclo-rotation of the eye (around the line of sight) can be predicted from the direction of the fixation point. It is shown here that Listing's law can be conveniently formulated in terms of rotation matrices. The function that defines the observed cyclo-rotation is derived in this representation. Two polynomial approximations of the function are developed, and the accuracy of each model is evaluated by numerical integration over a range of gaze directions. The error of the most simple approximation, for typical eye movements, is less than half a degree. It is shown that, given a set of calibrated images, the effect of Listing's law can be simulated in a way that is physically consistent with the original camera. This is important for robotic models of human vision, which typically do not reproduce the mechanics of the oculomotor system.