This paper presents a constitutive equation for masonry vaults which associates to each pair of generalized strains (A, K), where A are the strains, K are the curvature changes of the mean surface, the pair of generalized internal forces, (N, M) with N and M being the normal forces and bending moments per unit length, respectively The maximum modulus eccentricities surface is defined, and its main properties are proved. Subsequently, the limit analysis for masonry vaults is set forth and applied to the evaluation of the collapse load for a toroidal tunnel subjected to its own weight and an uniform load applied on the top circle.