The ultimate strength of reinforced masonry compression members subjected to axial or eccentric vertical loads is the main concern of the paper. As an initial step, the literature is reviewed so as to arrive at reasonable assumptions relating to the stress–strain properties of the material; these are necessary to define the load–moment interaction curve for a short column or wall. A method that can account for the weakening effect of slenderness is also discussed. These two fundamental components of the procedure are then judged relative to experimental test data. Axially loaded walls are modelled quite well but the theory is conservative for walls tested eccentrically. Although the inclusion of a strain gradient factor and consideration of nonlinear behaviour would improve analytical predictions for the latter case, these extra factors are not applied to the results due to a lack of definitive knowledge relating to the latter.