In this paper, the membrane and buckling analysis of beams with various shaped brackets is performed by using the finite element method. From the viewpoint of minimum structural weight, a optimum design method to determine the optimal shapes and scantling of brackets under design load is proposed by investigating the effects of beam depth, bracket length and aspect ratio on the structural weight. Also optimal design data and charts for the brackets to support transverse girders or web frames of actual ships are provided. By the present design method, it is possible to perform optimum design of brackets used in actual ships, which could result in considerable reduction of structural weight or cost, increase of dead weight and service speed of ships.