In the present work, a procedure for preliminary design optimization of a steam generator has been developed with the objective of minimizing the weight of the generator, Some real engineering constraints are considered in the problem formulation. A method of evaluating the objective function and constraints of the problem is presented. The problem has been solved numerically by using the exterior SUMT in which the Powell unconstrained minimization technique improved by Sargent with the parabolic interpolation method of one-dimensional minimization, is employed. The results of the optimum design and a sensitivity analysis conducted about the optimum point have been reported.