Ensuring the safety of the manned spacecraft crew and technical personnel work during the pre-launch preparation of manned launches at space launch complexes is an urgent problem. It can be solved by the development of emergency evacuation units (EEU), providing rescue of people in emergency on high-altitude units of launch complexes. The analysis of current research of EEU, made in Russia and the United States, showed that at the promising Russian space rocket complexes it is appropriate to use a rail EEU with a trolley moving along the guide system made in the form of the quickest descent curve – brachistochrone. According to the calculations, such a system can provide a minimum time of descent and removal of the trolley with people at a safe distance from the launch site, and also creates favorable conditions for damping the speed of the trolley on the final section of the descent trajectory. The study of the descent trajectory is for the first time based on the brachistichrone as applied to the EEU which allowed obtaining the calculated dependences necessary to determine the parameters of the guide system of the EEU, and to make recommendations for the design of such systems.