In this paper, we offer a stability analysis of "the cue interaction model" of depth perception (House (1984]. Depth estimation using stereopsis suffers from the "matching problem", the problem of correctly matching the retinal image of a feature in one eye, to its retinal image in the other eye. The Cue Interaction Model overcomes this by using monocular cues to disambiguate between the "correct matches" and the "incorrect matches". Its decision making is based on the concept of cooperation and competition in a neural network. A general class of cooperative and competitive models has been mathematically analysed by Amari and Arbib (1977), with special attention given to equilibrium states and stability. In this paper we adapt their methods to study the above model. In particular, we prove that if the parameters are correctly tuned, the model successfully achieves its goals by suppressing the cues which represent the "incorrect matches".