The response of load-bearing brick masonry walls is characterised by the second-order bending effects due to the eccentricity of the load, the non-linear compressive response of the masonry and its almost negligible tensile strength. Strengthening these structures is an interesting alternative to enhance their life-cycle. An experimental campaign has been carried out, consisting of tests on TRM (Textile Reinforced Mortar) strengthened walls. These have been tested under eccentric compressive loading conditions. The analysis has allowed studying the influence of the strengthening mortar type on the load-bearing capacity. The effects using anchors or embedding different types of fibre grids have been also analysed. A bidimensional (2D) simplified micro-model has been implemented to analyse these strengthened walls. This numerical tool has been validated using the data from the experimental campaign. Finally, an analytical methodology has been proposed to calculate the load-bearing capacity of TRM-strengthened brick masonry walls. The results show that the TRM provides a load-bearing capacity increase over 100% and homogenises the structural response.