An optimization for the geometrical parameters of continuous fins on an array of tubes of a refrigeration evaporator is developed in this paper using the exergy method. The method is based on exergy, economic analysis, and optimization theory. As there are humid air and refrigerant single- and two-phase streams involved in the heat transfer process, then there are irreversibilities or exergy destruction, due to pressure losses , due to temperature difference and due to specific humidity gradient . These principal components of total irreversibility are not independent, and their relative contribution to total irreversibility of a cross-flow refrigeration evaporator is investigated. A change in geometry was obtained by varying the evaporator tube diameter for a selected evaporator capacity, and hence the evaporator tube length and total heat transfer area are calculated for a fixed evaporator face length. In this way, the effect of changes in the geometry on the total number of exergy destruction units of the heat exchange process is investigated. The optimum balance between the three components of irreversibility (, and ) is also determined, thereby giving the optimum solution for the heat exchanger area. The total cost function, which provides a measure of the contribution of the evaporator to the total cost of the refrigeration system, is expressed on the basis of annual capital and electrical energy costs. The total cost function is minimized with respect to the total heat transfer area and the total number of exergy destruction units . The relationship between the operational variables, heat transfer area, refrigerant and air irreversibilities, and the total annual cost for this type of evaporator are developed, presented, and discussed. The pressure, temperature, and specific humidity irreversibilities are found to be 30.34%, 33.78%, and 35.88%, respectively, of the total irreversibility, which is 8.5% of the evaporator capacity.