An experimental and numerical research on the characterization of the capacity of load bearing brick masonry walls taking into consideration the non-linear geometric effects and the buckling failure is presented. Experimental results obtained by different authors have been reviewed and numerically simulated by means of a micro-modelling approach. A detailed parametric study has been carried out to extent the results to a larger range of cases regarding the material properties, the wall geometry and the loading conditions. Based on it, a set of new empirical equations has been obtained for the estimation of capacity of masonry walls taking into account the load eccentricity, the wall slenderness ratio, the masonry stiffness and the masonry tensile strength. In addition, a new formulation resulting from the application of an artificial neural network on the results of the parametric study is also presented. The different equations proposed show a satisfactory agreement with the experimental results and are considered suitable for their application to the design and verification of brick masonry load bearing masonry walls.