This paper presents a disjunctive mathematical model for the optimal design of air cooled heat exchangers. The model involves seven discrete decisions which are related to the selection of the type of the finned tube, number of tube rows, number of tube per row, number of passes, fins per unit length, mean fin thickness and the type of the flow regime. Each discrete decision is modeled using disjunctions, boolean variables and logical propositions. The main continuous decisions are: fan diameter, bundle width, tube length, pressure drops and velocities in both sides of the ACHE, heat transfer area, fan power consumption. Then, the resulting generalized disjunctive programming model is reformulated as a mixed integer non-linear programming, implemented in GAMS (general algebraic modeling system) and solved using a branch-and-bound method. The proposed model was successfully verified by comparing the obtained output results with different designs taken from the literature. Then, the model is solved to obtain the optimal designs corresponding to the following optimization criteria: a) minimization the total annual cost which includes investment (heat transfer area) and operating cost (fan power consumption), b) minimization the heat transfer area and c) minimization the fan power consumption. Obtained optimal and sub-optimal designs are compared in detail. Crown Copyright (C) 2013 Published by Elsevier Ltd. All rights reserved.