Steller's sea cow, a giant sirenian discovered in 1741 and extinct by 1768, is one of the few megafaunal mammal species to have died out during the historical period. The species is traditionally considered to have been exterminated by 'blitzkrieg'-style direct overharvesting for food, but it has also been proposed that its extinction resulted from a sea urchin population explosion triggered by extirpation of local sea otter populations that eliminated the shallow-water kelps on which sea cows fed. Hunting records from eighteenth century Russian expeditions to the Commander Islands, in conjunction with life-history data extrapolated from dugongs, permit modelling of sea cow extinction dynamics. Sea cows were massively and wastefully overexploited, being hunted at over seven times the sustainable limit, and suggesting that the initial Bering Island sea cow population must have been higher than suggested by previous researchers to allow the species to survive even until 1768. Environmental changes caused by sea otter declines are unlikely to have contributed to this extinction event. This indicates that megafaunal extinctions can be effected by small bands of hunters using pre-industrial technologies, and highlights the catastrophic impact of wastefulness when overexploiting resources mistakenly perceived as 'infinite'.