In this paper, the sizing method and reference battery state of charge (SOC) trajectory for a hybrid aircraft under failure conditions are presented. With this aim, first, the types of hybrid-electric propulsion system (HEPS) structures along with their components are introduced. Then, the failure modes of HEPS main components and their impact on the aircraft performance are investigated. Next, the sizing of parallel HEPS under all-turbine and battery pack failures is formulated. Then, the reference SOC trajectory is presented by simulating the HEPS during a real flight mission, to ensure the safe landing of the aircraft in the event of all-turbine failure. So that the battery SOC in the cruise and descent phases should be about 35-45% and 65%, respectively. Finally, using the results of the parallel hybrid aircraft simulation under emergency failure modes, the correctness of the proposed sizing procedure has been proven. In addition, by presenting the simulation results of the healthy hybrid aircraft, the satisfaction of the performance constraints of the parallel HEPS has been validated.