Developed for applications in itemset mining, the notion of Mutual Constrained Independence is a natural generalization of the notion of mutual independence. If the mutual independence model on a finite number of events can be seen as the least binding model for the probabilities of any finite intersection of these events, given the probabilities of each of these events, then the Mutual Constrained Independence Model on a finite number of events can be seen as the least binding model for the probabilities of any finite intersection of these events, given the probabilities of any number of such intersections of events. In this article, we present a first detailed and effective means of computing the Mutual Constrained Independence Model. We show the efficiency of our algorithm and the adequacy of the model by applying it to various examples. A test for the Mutual Constrained Independence Hypothesis is also presented.