The problem of finding the position of two membranes, one constrained by the other, attached to rigid supports, subjected to external forces, is considered. It is proved existence of solution, if we assume a compatibility condition relating the mean curvature of the boundary of the set where the problem is defined and the given data. It is also proved the W^{2,p} regularity of the solution for P greater or equal to 1.Fundação para a Ciência e a Tecnologia (FCT
