Mammoths were an important resource for Upper Palaeolithic hunter-gatherers. Their remains are frequently found in faunal assemblages, their bones were used for the construction of dwellings, and they figure significantly in Palaeolithic art. Mammoths became extinct in North America at ca. 11,000 BP, in Eurasia at ca. 12,000 BP, and in Siberia at ca. 10,000 BP, and there has been considerable debate as to whether human predation was a causal factor. The computer simulation model described in this paper explores the effect of different types of hunting strategies on mammoth populations in a range of different environmental situations. It demonstrates that mammoth populations are extremely sensitive to predation. The simulation results are discussed with reference to the settlements on the Central Russian Plain. The results agree with Soffer's suggestion that the majority of mammoth remains probably derive from collecting, rather than hunting.