A special class of steel plates, called bracket plates, is commonly used for brackets and stiffeners. Designing these structural elements has proved to be a complex problem involving many parameters and different types of behaviour. The methods used for design are often conservative and simplified because the subject has received little attention. This paper attempts to shed light on the problem and develop a new and improved design method for triangular bracket plates, derived on the basis of a consistent theory. The new design method proposed is based on the theory of plasticity, practically the yield line theory. Using the new method to solve the buckling problem for bracket plates leads to a method that, compared with existing test results, supplies very good results.