Reinforced brick masonry has experienced only scarce use as a fully structural material due to, among other reasons, the lack of design criteria and calculation tools allowing a scientific, but also practical, engineering approach to design and assessment. Aiming at contributing to a more widespread use of this material, a simplified method for the ultimate analysis of reinforced masonry arches and cylindrical vaults, based on the lower-bound theorem (or static approach) of plasticity, has been developed. This approach has been satisfactorily validated by comparison with experimental and numerical results obtained by more accurate numerical models