Optimum design analysis in engineering is generally formulated as a problem of nonlinear programming. For casing design problem, there are combinatorial variables, integer variables, which select a casing to be used among alternatives. In spite of including integer variables, nonlinear programming may be able to optimize the casing design problem, since it has an enough optimization potential for continuous variable problem. In this paper, an application study is presented to verify the usefulness of nonlinear programming termed SUMT for casing design problem.