The paper deals with a experimental and numerical study of a masonry barrel vault subjected to an incremental horizontal settlement of one abutment. The analyzed vault is very slender and with no backfill, as is typical of the vaulted roofs covering many Italian churches and other religious buildings of various dimensions, that often suffer a certain amount of settlement due to the deformation of the sustaining walls. The experimental tests have been conducted at the University of Florence on a full-scale specimen. The vault, firstly damaged by increasing the magnitude of the imposed settlement, has been then repaired with a FRCM system composed by a inorganic mortar embedding a uni-directional PBO fiber net applied at the intrados, and tested again. In this paper, the experimental tests has been assumed as a benchmark, and numerical simulations have been carried out by means of different models, some implemented in the general purpose FEM software Abaqus, and others specifically developed for masonry structures. The capability of the considered models to describe the actual behavior of the vault in its unstrengthened and strengthened configuration has been investigated, and their potential highlighted.