An inverse design method is presented which determines the proper size, shape, and location of coolant flow passages in composite ceramic/metal scram jet combustor struts. In this work, an optimization technique is coupled with the boundary element method to produce an inverse design procedure for multi-holed, internally cooled scram jet combustor struts. This inverse design technique is demonstrated for several examples of internally cooled scram jet combustor struts in order to prove the feasibility and accuracy of the method. This numerical technique readily applies to other inverse design problems and configurations involving heat transfer.