We consider a linearly elastic shell with a hyperbolic, or parabolic, middle surface, clamped along a large enough portion of its lateral face and sub- jected to body forces. We then show that the two-dimensional limit model found by the asymptotic analysis from the three-dimensional shell problem is the “gen- eralized membrane” shell model, according to the terminology introduced by P.G. Ciarlet and V. Lods. We also identify the functional space where this model is well posed.