Background The pace of aging varies considerably in nature. The best-known explanation of the evolution of specific rates of aging is the Williams' hypothesis suggesting that the aging rate should correlate with the level of extrinsic mortality. However, the current evidence is inconclusive with various examples where the Williams' hypothesis seems to be correct and where it doesn't. Here we explore the relationship between extrinsic mortality and aging rate by developing a simulation model of the evolution of aging rate in prey subject to predation. Results Our results suggest that more intense predation leads to the evolution of faster pace of aging in prey. However, this effect slowly vanishes when the predator diet breadth is allowed to evolve, too. Furthermore, in our model, the evolution of a specific aging rate is driven mainly by a single parameter, the strength of a trade-off between aging and fecundity. Indeed, in the absence of this trade-off the evolutionary impacts of predation on the prey aging rate appear random. Conclusions We show that the William's hypothesis appears valid when there is a trade-off between aging and fecundity and predators and prey do not coevolve. However, we also show that when the prey and predators coevolve or if there is no trade-off between aging and fecundity the William`s hypothesis is no longer applicable.