This study analyzes an Allam cycle by means of analytical modeling. In a recent ASME Turbo Expo Conference (Turbo Expo 2020), an analytical formulation was presented for the net power output of a natural gas fired Allam cycle with an uncooled turbine. An algebraic expression was derived for optimum turbine inlet temperature (TIT) maximizing the cycle efficiency. In practice, TIT is constrained by durability of the turbine blade material with a maximum allowable temperature of 860 °C as reported by the cycle developers. The objective here is to determine optimum turbine inlet and exhaust pressures by maximization of the cycle efficiency subject to a fixed temperature at the combustor outlet. To avoid complexity of the analysis, reasonable simplifications are considered including negligible temperature and pressure drops between adjacent components. Analytical expressions are obtained for optimum pressure of the combustion gases at the inlet and outlet of the turbine meaning that the net cycle efficiency can be twice optimized. The optimum turbine exhaust pressure is found to be a function of (TITηtηc/Tc) where Tc denotes a cycle minimum temperature and η is the isentropic efficiency. The new expressions are used to calculate the optimum turbine inlet pressure, exhaust pressure, and maximum cycle efficiency for a practical range of the combustion temperature and varying pressure at the exit of the CO2 compressor. The relations derived in this study provide (i) a solid foundation for those unfamiliar with Allam cycle, and (ii) a useful tool for engineers to roughly estimate optimum operational regime of the cycle without a need for complex calculations.