A systematic multi-step method was developed for selection of the best working fluid(s) for the simple and regenerative Brayton cycles. The first step of the method involves development of the thermodynamic model of a cycle and development of theoretical expressions for its thermodynamic performance (thermal efficiency and net specific work output). In the second step, parametric calculations were performed for nine working fluids over a range of cycle operating conditions corresponding to the concentrated solar power plants (CSPs) to determine the effect of cycle operating conditions and thermo-physical properties of the working fluids on cycle performance. The statistical regression analysis is used in the third step to develop correlations for the cycle efficiency and net specific work of the same form as theoretical expressions developed in Step 1. The last step in the process involves construction of performance maps, where performance parameters, such as thermal efficiency and net specific work output are presented as functions of the cycle operating conditions. The performance map for thermal efficiency shows that, depending on the operating conditions, either N-2 or CO2 are the best choices of the working fluids. However, considering the net specific work output, He is the best working fluid over the entire analyzed range of the cycle operating conditions.