The research addressed in the paper is aimed at calibrating a numerical model developed by using a free open-source finite-element code for the assessment of the structural performances of historical masonry buildings strengthened using the textile-reinforced mortar (TRM) technique. TRM is a near-surface-mounted system, which couples inorganic matrices with fiber-based textile or meshes. The main purpose is to develop a multiple-level numerical approach, starting with the detailed modeling of components and interfaces, followed by a computationally efficient intermediate level model, using layered elements, for the calibration of a lumped plasticity-based model suitable for the global analysis of structures. In this paper, the first research results are presented. In particular, a broad literature review concerning the mechanical characterization and analysis of TRM systems is collected. Then, the calibration of the numerical model, the validation through comparison with the results of experimental characterization tests available in the literature (tensile, shear bond, and in-plane shear tests) and a sensitivity analysis are reported. Nonlinear static analyses were performed, considering the nonlinearity of the composite material components and interfaces. The model was capable of accounting for the main parameters affecting the behavior of the composite material, such as the reinforcement ratio and orientation, the mortar characteristics and the wire-mortar interaction and proved to be a valid tool to investigate the optimization of TRM applicative details.