In this paper a mixed integer non-linear programming (MINLP) model is proposed for the design of shell and tube heat exchangers. The model rigorously follows the TEMA (Tubular Exchanger Manufacturers Association) Standards and Bell-Delaware Method is used to the shell side calculations. Mechanical design features (shell and tube bundle diameters, internal and external tube diameters, tubes length, pitch and tube arrangement, number of tubes and tube passes) and thermal-hydraulic variables (heat, area, individual and overall heat transfer coefficients, shell and tube pressure drops and fouling) are variables to be optimized. The equipment is designed under pressure drop and fouling limits. Three cases from the literature are studied, with two different objective functions, considering just the heat transfer area minimization or the annual cost minimization, including area and pumping expenses. More realistic values are obtained when compared with the literature, considering fouling and pressure drop effects according to TEMA Standards.