Abstract In many engineering applications the limit analysis theorems can be used to estimate the ultimate capacity of several structures. However, the limit analysis can be applied on structures with an adequate plastic capacity. When the goal is to evaluate the ultimate capacity of masonry structures, they could show some drawbacks. For this reason, the incremental analysis represents a valid alternative to estimate the ultimate capacity of masonry structures. These structures could show brittle failures before the hinge mechanism. It is a key aspect especially for curved masonry elements like as arches and vaults. The work focuses on the incremental analysis of masonry barrel vaults without backfill. An analytical model in the framework of the incremental analysis has been proposed. The analytical model allows to assess both the ultimate capacity and the ductility of the masonry barrel vaults. In the first part, the proposed model has been discussed. Then, parametric analysis was performed to assess the impact of physical, geometrical and mechanical parameters on the ultimate behaviour. The numerical results allow to identify some structural examples where the brittle behaviour becomes crucial. Finally, the proposed model was validated with experimental results on a full-scale masonry barrel vault. Highlights • The work focuses on the incremental analysis of masonry barrel vaults without backfill, accounting for tensile strength. • The analytical model allows to assess both the ultimate capacity and the ductility of the structure incrementally. • The numerical results allow to identify some structural examples where the brittle behaviour becomes crucial. • The proposed model was validated by using the experimental tests of a masonry barrel vault actually tested. [ABSTRACT FROM AUTHOR]