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Historic masonry characterizes large part of the building heritage in Europe and worldwide but may suffer for structural weaknesses related to material deterioration, long-term fatigue, over-time modifications, accidental actions, seismic vulnerability... For the structural refurbishment of these building assets, the use of fiber-based composites has widely spread within the last twenty years as strengthening strategy. In particular, the coupling of fiber-based meshes or textiles with mortar plasters (the so-called Textile Reinforced Mortar technique) gained great relevance due to effectiveness, easiness of installation, compatibility of materials, durability and reversibility. The development of design methods for this new technique requires, beside a robust experimental database, also reliable and optimized numerical strategies for the performance estimations. In this context, the paper introduces a simplified finite-element modelling approach, based on multi-layered 3D elements, for the assessment of the structural performances of masonry assemblages strengthened with Textile Reinforced Mortar (TRM). In particular, the free, open source, finite element code OOFEM is adopted to perform non-linear static analyses of masonry samples subjected to in-plane or out-of-plane actions. Brick elements with laminated material composition are adopted for the simulations, with layers stacked along the sample thickness: the inner layer for the masonry and a couple of outer layers for the plaster and for the fiber-based reinforcement. The Gauss integration rule is used for setting up integration points in each layer, which number can be specified independently for each layer. The materials mechanical parameters for each layer are set in accordance to the results of experimental characterization tests available in the literature. The reliability of the simulations is assessed through comparison with previous experimental outcomes concerning tests on TRM strengthened masonry elements, namely diagonal compression tests, in-plane three-point bending tests and out-of-plane four-point bending tests. The model is feasible to reproduce the typical failure modes of masonry elements for both in-plane actions (diagonal cracking and in-plane bending failure) and out-of-plane actions (out-of-plane bending failure) also at advanced damage levels and thus can represent a useful and optimized tool to investigate on wider samples, such as entire walls with openings, even under combined in-and out-of-plane loading. [ABSTRACT FROM AUTHOR]