My study examines a category of data--the logistics of classical Greek warfare--that has not been used before for ancient Greek economic history. This examination provides much new evidence for Greek economies in the fifth and fourth centuries. Close readings of contemporary literary evidence--especially Thucydides--shows that classical Greek amphibious and naval expeditions military forces always acquired their food from markets provided to them by cities and traders. A systematic comparative analysis confirms this conclusion by demonstrating that the economic and politico-social structures of classical Greek states meant that the market was the only institutional mechanism available to them to feed their navies and amphibious forces--in contrast to other European and near Eastern pre-industrial states which could use mechanisms such as requisitioning and taxation-in-kind to acquire provisions to supply their military forces. I then produce estimates of the amounts of food purchased by classical Greek military forces in the markets provided to them by cities and traders by combining data on standard daily rations (from contemporary literary and epigraphical sources) and caloric requirements (established from an analysis of classical Greek skeletal material and WHO/FAO research data) with the relatively precise figures we have in contemporary historians for army and navy sizes and lengths of campaigns. These calculations provide many more figures for trade in grain and other foods in the classical period than we currently possess, and figures that are mostly much greater in scale. The analysis of the provisioning of Greek overseas warfare provides, then--for the first time--evidence for a regular and large-scale seaborne trade of grain in the classical Greek Mediterranean; it shows a world where the development of marketing structures and networks of merchants was sufficiently strong to permit tens of thousands of men to get their food through markets for years at a time. Demonstrating the existence of a regular and substantial overseas trade in grain in the fifth and fourth centuries is crucially important for a wider understanding of classical Greek economies because the existence of such a trade made possible increased urbanization and specialization of labor, and itself could only have been made possible by sizeable reductions in transactions costs for maritime commerce: it therefore provides evidence for the foundations of economic growth in classical Greece