We introduce a parsimonious multi-sector model of international production and use it to study how a disruption in the production of intermediate goods propagates through to final goods, and how that impact depends on the goods' positions in, and overall structure of, the production network. We show that the short-run disruption can be dramatically larger than the long-run disruption. The short-run disruption depends on the value of all of the final goods whose supply chains involve a disrupted good, while by contrast the long-run disruption depends only on the cost of the disrupted goods. We use the model to show how increased complexity of supply chains leads to increased fragility in terms of probability and expected short-run size of a disruption. We also show how decreased transportation costs can lead to increased specialization in production, with lower chances for disruption but larger impacts conditional upon disruption.