The boundary integral equation method (BIEM) of analysis was applied to problems involving beams, thick plates and stress concentration regions. Beam and plate problems were considered to provide guidelines for use of the three-dimensional BIEM to analyze brackets and other components which have “solid like” regions as well as regions which are “beam or plate like”. In unsubstructured form the BIEM produced results in excellent agreement with exact solutions from elasticity theory for plates with length/thickness ratios as large as 40. Loading cases included bending by terminal couples and flexure by terminal loads. Using substructuring, CP times were reduced. CP times for both the IBM 3084 and the CDC CYBER 205 were obtained, the influence of varying integration orders discussed, and techniques to assess the accuracy of computed results were described. The BIEM was also found to produce accurate stress concentration factors for tension, bending and torsion of a round bar with a U-shaped circumferential groove.