Optimal design of shell and tube heat exchanger system with the working fluids which may condense outside the tubes has been carried out under specified inlet and outlet conditions. Independent variables such as number of parallel series, tube diameter, distribution pitch, tube side pressure loss, baffle cut and shell side pressure loss as well as dependent variables such as shell diameter, number of tubes, number of serial series and number of baffles were all characterized according to the standard. Exhaustive search method was used to construct a computer program together with the calculation of heat transfer rate by LMTD method. stress analysis of maj or parts was made to examine their dimensions satisfying heat transfer and pressure loss requirements. Cost estimation based on the installation, operation and maintenance was also made, A few representative variables, heat transfer area, shell diameter and pressure loss, were used to express cost function, finally giving the optimal selection of all tentative solutions.