Advance market commitments (AMCs) provide a mechanism to stimulate investment by suppliers of products to low-income countries. In an AMC, donors commit to a fund from which a specified subsidy is paid per unit purchased by low-income countries until the fund is exhausted, strengthening suppliers’ incentives to invest in research, development, and capacity. Last decade saw the launch of a $1.5 billion pilot AMC to distribute pneumococcal vaccine to the developing world; in the current pandemic, variations on AMCs are being used to fund COVID-19 vaccines. This paper undertakes the first formal analysis of AMCs. We construct a model in which an altruistic donor negotiates on behalf of a low-income country with a vaccine supplier after the supplier has sunk investments. We use this model to explain the logic of an AMC — as a solution to a hold-up problem — and to analyze alternative design features under various economic conditions (cost uncertainty, supplier competition). A key finding is that optimal AMC design differs markedly depending on where the product is in its development cycle.