For an endoreversible heat engine operates steadily between two fixed temperatures, Bejan found the engine's best performance can be obtained if the total thermal conductance is evenly divided for hot-end and cold-end heat exchangers. In this study, a heat by-pass model is used to represent the losses due to internal irreversibilities, and the more general formulations are derived for both the optimal area allocation and the maximum thermal efficiency. The results calculated from the present formulations when there is no internal irreversibility(a special case) are consistant with that obtained by Bejan.