A Finite Element Method (FEM) based model is presented that can be applied as a limit-analysis tool for vault surfaces and other masonry shell structures. The absence of tensile strength in such structures results in a further non-linear mechanical behaviour. The model can find the collapse mechanism of an arbitrary, symmetrical surface geometry by developing the openings (cracks) between the elements, which gradually reduce the structure’s initial stiffness. The limit load is measured when the structure becomes a mechanism globally or locally. The method is illustrated on a hemispherical dome, whereas the effects of material properties and the presence of structural damage (cracks caused by past effects) are investigated. The presented model can evaluate existing or theoretical historical vault geometries and might help to determine the effective way of strengthening.