In this paper, a simple model is proposed for the non-linear analysis of cloister vaults subjected to strip loads. The geometry is implemented in a homemade FE element software where bricks are assumed elastic and the nonlinearity is concentrated in the mortar joints. The joints are treated as interfaces with finite thickness, where a coupled mode 1 and mode 2 failure (Mohr Coulomb Cohesive Frictional Relationship) is possible. In addition, the model is linked to a 16-degree-of-freedom finite element capable of simulating a reinforcement with Fiber Reinforced Cementitious Matrix (FRCM). The aim is to evaluate the increase in the load-bearing capacity when such type of strengthening material is applied. The procedure is benchmarked on an existing cloister vault present in the former Monastery of Santa Maria della Pace in Piacenza, Emilia Romagna, Italy. The vault exhibits a pre-existing structural damage not only due to the consequences of the 2012 earthquake that hit Emilia Romagna, but also for the presence of a heavy masonry wall insisting at the middle span. After a careful analysis of the results obtained in terms of load-displacement curves, and a comparison between the reinforced and unreinforced case, the reliability of the proposed approach is shown.