Influenza pandemics present a global threat owing to their potential mortality and substantial economic impacts. Stockpiling antiviral drugs to manage a pandemic is an effective strategy to offset their negative impacts; however, little is known about the long-term optimal size of the stockpile under uncertainty and the characteristics of different countries. Using an epidemic-economic model we studied the effect on total mortality and costs of antiviral stockpile sizes for Brazil, China, Guatemala, India, Indonesia, New Zealand, Singapore, the UK, the USA and Zimbabwe. In the model, antivirals stockpiling considerably reduced mortality. There was greater potential avoidance of expected costs in the higher resourced countries (e.g. from $55 billion to $27 billion over a 30 year time horizon for the USA) and large avoidance of fatalities in those less resourced (e.g. from 11.4 to 2.3 million in Indonesia). Under perfect allocation, higher resourced countries should aim to store antiviral stockpiles able to cover at least 15 per cent of their population, rising to 25 per cent with 30 per cent misallocation, to minimize fatalities and economic costs. Stockpiling is estimated not to be cost-effective for two-thirds of the world's population under current antivirals pricing. Lower prices and international cooperation are necessary to make the life-saving potential of antivirals cost-effective in resource-limited countries.