Numerical optimization of heat and fluid flow over staggered tube banks are investigated for both unfinned and axially finned tube banks. Ansys Fluent software is utilized for numerical computations. To find maximum total heat transfer and minimum volume of tube bank for the given mass flow rate, allowable pressure drop and tube bank effectiveness; A Multi-objective Genetic Algorithm II is used. Optimum designs are given on tabular forms and variations of total heat transfer with total volume are presented. Moreover, effects of transversal and longitudinal pitches on objective functions are graphically demonstrated. In order to confirm reliability of the numerical studies, unfinned staggered tube bank configuration is compared with experimental studies in literature. As a result of optimization studies, axial fin usage results in 42.7% decrement in volume of staggered tube bank with respect to unfinned case, while heat transfer values are equal with maximum obtainable heat transfer rate for the given optimization problem.