Fibre Reinforced Polymers laminates are currently used to strengthen brick masonry walls. However, no specific evidences of the structural response of this strengthening system when brick walls are subjected to eccentric compressive loads, which might lead to second order bending effects, have been found. An experimental campaign on real-size walls has been carried out and the results have been compared with a numerical model, which predicted the observed shear/compressive masonry failure, and a new analytical approach, which has been used to accurately calculate the load-bearing capacity of the walls. Useful considerations for the strengthening design are also presented.