A new procedure for the nonlinear static analysis of curved masonry structures characterised exclusively by flexural failure is presented. It is developed to be exploited in commercial Finite Element software and put at the common user’s disposal. Three steps define the methodology used. In the first one, a standard mesh is constructed using hexahedral elements assigned with two materials, namely elastic masonry and non-linear interfaces with thickness (joints). Then, in step two, the discretisation obtained is imported into a homemade software conceived for this purpose, serving as an automatic pre-processor and working on the already existing standard mesh. It aims to convert automatically the thick interfaces meshed with hexahedrons into an assemblage of rigid beams and axial and tangential cutoff bars (trusses). The axial bars exhibit finite strength, while the shear ones are (up to now) infinitely resistant. This combination of fragile or, in turn, ductile cutoff bars enables the consideration of contemporarily flexural cracking inside the joints and the actual elastic shear stiffness, thus lumping flexural nonlinearities inside the thick interfaces. The final step consists of importing the output of the homemade code into whatever low-cost finite element software, equipped only with non-linear trusses and elastic hexahedra, to perform standard static non-linear analyses. The procedure is benchmarked against one example of an in-situ tested masonry arch for which a variety of results is available in the literature. The robustness of the approach is proved after an in-depth analysis of the resulting force-displacement curves and of the failure mechanisms triggered.