The traditional half-brick, one-brick and standard cavity wall have been designed successfully for many years using the design guidance contained in the BS Codes of Practice. The method, however, does have some limitations. These stimulated the search for a new prediction equation. The suggested approach, which is based on a pin-ended model, is developed using a modified Rankine theory. Capacity reduction factors are derived which are similar in value, but not identical with, the ß values in BS 5628: Part 1. The approach appears to predict the behaviour of masonry walls better than the present Code guidance when the full range of slenderness ratios, for which some test results are available, is considered. The major advantage of the approach lies in the fact that the capacity reduction values can be written in terms of L/r slenderness ratios and Z/A eccentricity ratios. This could permit the designer the ability to determine, using one table of capacity reduction factors, the design load resistance of any solid wall or any other wall or column of irregular geometry. The method proposed does place a limit on the eccentricity of the applied load on walls of irregular planform: it must lie within the kern of the section. The design approach could be applied to vertically loaded members which also carry lateral loads, and the method permits the design of columns in biaxial bending. By assuming a ‘no tension’ material and by ignoring any cracked masonry in tension, a lower bound solution can be obtained for any non-planar wall with a highly eccentric load.