The design process of shell and tube heat exchanger is difficult due to the complex geometric parameters with thermodynamic and fluid dynamic factors, which consume more time and minimum possibility for an optimum result in the case of conventional design. The optimum design of shell and tube heat exchanger was determined to predict optimum heat transfer coefficient with the effect of geometrical parameters such as number of baffles (NB), Shell diameter (Ds), Tube pitch (Pt) and Baffle spacing (LB). The analytical calculations were done using Response Surface Methodology on four factors, three level, central composite face centered design matrix with full replications technique by 95% confidence level. The results indicate that the geometrical parameters with optimum design.