The historical regulation of African elephant Loxodonta africana populations could provide guidelines for management efforts and decisions in areas where elephant numbers are now increasing. However, there are few detailed records of the natural mortality processes of the past. Therefore, we modelled elephant population growth to evaluate possible effects of age-specific mortality. Model projections indicated that an annual mortality of 17.1% of juveniles or 10.5% of adults would be sufficient to prevent population growth. For age classes below or just at sexual maturity (i.e. 0-3, 4-7, 8-11) 37.5% annual mortality of one of these classes was required to achieve 0% population growth. These mortality levels are much higher than those reported in southern Africa today. Simulations of episodic mortality events (e.g. droughts) indicated that such events would need to occur every 16 years at a severity that would cause the mortality of all infants and weaned calves (0-7 years old), as well as 10% of adults and subadults (8-60 years old) to prevent long-term population growth. An 8-year frequency required the mortality of 84.7% of infants and weaned calves. Historically, it is possible that high drought mortality and frequency, and high predation levels, may have reduced population growth significantly but current mortality rates and frequencies are insufficient to constrain long-term average population growth at 0%. The natural limitation of existent elephant populations through mortality is therefore unlikely, indicating a need for active management of the increasing elephant populations in southern Africa.