This paper addresses numerical modeling and nonlinear analysis of unreinforced masonry walls and vaults externally strengthened using fiber reinforced polymers (FRP). The aim of the research is to provide a simple method for design of strengthening interventions for masonry arched structures while considering the nonlinear behavior. Several brick masonry walls and vaults externally strengthened by FRP which have been previously tested experimentally are modeled using finite elements. Numerical modeling and nonlinear analysis are performed using commercial software. Description of the modeling, material characterization and solution parameters are given. The obtained numerical results demonstrate that externally applied FRP strengthening increased the ultimate capacity of the walls and vaults and improved their failure mode. The numerical results are in good agreement with the experimentally obtained ultimate failure load, maximum displacement and crack pattern; which demonstrates the capability of the proposed modeling scheme to simulate efficiently the actual behavior of FRP-strengthened masonry elements. Application is made on a historic masonry dome and the numerical analysis managed to explain its structural behavior before and after strengthening. The modeling approach may thus be regarded a practical and valid tool for design of strengthening interventions for contemporary or historic unreinforced masonry elements using externally bonded FRP