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In this work, two main fiber strengthening systems typically applied in masonry structures have been investigated: composites made of basalt and hemp fibers, coupled with inorganic matrix. Starting from the experimental results on composites, the out-of-plane behavior of the strengthened masonry was assessed according to several numerical analyses. In a first step, the ultimate behavior was assessed in terms of P (axial load)-M (bending moment) domain (i.e., failure surface), changing several mechanical parameters. In order to assess the ductility capacity of the strengthened masonry elements, the P-M domain was estimated starting from the bending moment-curvature diagrams. Key information about the impact of several mechanical parameters on both the capacity and the ductility was considered. Furthermore, the numerical analyses allow the assessment of the efficiency of the strengthening system, changing the main mechanical properties. Basalt fibers had lower efficiency when applied to weak masonry. In this case, the elastic properties of the masonry did not influence the structural behavior under a no tension assumption for the masonry. Conversely, their impact became non-negligible, especially for higher values of the compressive strength of the masonry. The stress-strain curve used to model the composite impacted the flexural strength. Natural fibers provided similar outcomes, but a first difference regards the higher mechanical compatibility of the strengthening system with the substrate. In this case, the ultimate condition is due to the failure mode of the composite. The stress-strain curves used to model the strengthening system are crucial in the ductility estimation of the strengthened masonry. However, the behavior of the composite strongly influences the curvature ductility in the case of higher compressive strength for masonry. The numerical results discussed in this paper provide the base to develop normalized capacity models able to provide important information on the out-of-plane behavior of masonry elements strengthened with inorganic matrix and several kinds of fibers, both synthetic and natural. more...