Abstarct: The heat transfer and pressure drop are two important parameters in heat exchanger design. This thesis presents an optimization of a shell and coiled tube heat exchanger. In most engineering problems purposes of optimization are not achievable simultaneously. It means that improvement of a purpose results in undesirable condition for second one. So a set of results will be obtained as ‘Pareto Front’. In this study, effectiveness is considered as an objective function as it includes heat transfer of tube side as well as heat transfer of shell side in a correlation. Also pressure drop is considered as second objective function. Tube radius, coil radius and coil pitch were considered as three design parameters. For optimal design of a shell and coiled tube heat exchanger, it was first thermally modeled using ε–NTU method. Non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) were applied to obtain the optimum results for objective functions. The results of optimal designs for effectiveness and pressure drop were presented as a set of multiple optimum solutions called Pareto front.