Finite-time thermodynamics has been applied to optimize the power output of endoreversible Brayton cycles with regeneration for infinite thermal capacitance rates of the heat reservoirs. The effect of regeneration on the thermal efficiency and power of endoreversible Brayton cycles is determined. The regenerative heat-transfer rate is positive for low temperature ratios and negative for high temperature ratios. The maximum power and the corresponding thermal efficiency are decreased by the use of regenerators. The second-law efficiency at maximum power decreases as the number of transfer units of regenerative heat transfer is increased.