The boundary integral equation method (BIEM) of analysis was applied to problems involving thick plates and stress concentration regions. In unsubstructured form the BIEM produced results in agreement with exact solutions from elasticity theory for plates with length/thickness ratios as large as 40, for the case of bending by terminal couples. Using substructuring, CP times were reduced. CP times for the CDC CYBER 205 were obtained, and the influence of varying integration orders was discussed. The BIEM was also found to produce accurate stress concentration factors for tension, bending and torsion of a stepped round bar with a circumferential shoulder fillet.