This study develops a practical supply and demand model of bilateral trade flows. The model is constructed in two tiers. First, aggregate import demand and aggregate export supply are determined from aggregate economic relations that contain real income (output) and relative prices. Second, bilateral import demand and bilateral export supply are determined from theory-based allocation relations. By differentiating import prices from export prices, the analysis incorporates international transportation costs and tariffs. The result is a simultaneous system that determines bilateral trade flows and bilateral prices given country incomes, domestic price levels and international transmission factors. The model in dynamic form is estimated from a panel of bilateral trade flows for five major OECD countries (United States, Japan, France, West Germany, United Kingdom) for the years 1958-1971. The model has many applications, e.g. in the analyses of the impacts on trade flows of differential economic growth rates and tariff policies. These policy aspects figure prominently in the current discussions among the major OECD countries.