We offer a new explanation as to why international trade is so volatile in response to economic shocks. Our approach combines the uncertainty shock idea of Bloom (2009) with a model of international trade, extending the idea to the open economy. Firms import intermediate inputs from home or foreign suppliers, but with higher costs in the latter case. Due to fixed costs of ordering firms hold an inventory of intermediates. We show that in response to an uncertainty shock firms optimally adjust their inventory policy by cutting their orders of foreign intermediates disproportionately strongly. In the aggregate, this response leads to a bigger contraction in international trade flows than in domestic economic activity. We confront the model with newly-compiled monthly aggregate U.S. import data and industrial production data going back to 1962, and also with disaggregated data back to 1989. Our results suggest a tight link between uncertainty and the cyclical behavior of international trade.