Recent climatic events and conflict have heightened concern about the vulnerability of the global food system to systemic shocks. Yet it remains unclear what shocks are most pressing for a country’s food supply, and whether trade can mediate or amplify negative impacts. Here, using a newly developed global bilateral trade model for 177 countries and four major staple crops (maize, wheat, rice, soybean), we simulate the demand, price and trade impacts of the (i) Ukraine war, (ii) an energy price shock, (iii) imposed trade bans, and (iv) a compound (polycrisis) shock, on top of 54 years of crop production variability. The compound shock results in a 23 – 52% increase in consumer prices and, consequently, 7.3 – 16.5% loss to consumers. While the energy price shock is found to be the most important driver of the compound food shock across most regions and crops, the Ukraine war dominates impacts in Eastern Europe and Central Asia. Trade bans can affect certain regions disproportionately, particularly for Sub-Saharan Africa (rice) and Central Asia (rice, wheat). We find that, in many instances, trade adjustments can help cope with both supply and price shocks, although limits to the reliance on trade are found for tail risk events. In the compound shock event, the total negative consumer losses can be over USD 600 million for a single year, affecting virtually all countries simultaneously. Managing the risks of such shocks requires a reformed and better coordinated mix of national agricultural and fiscal policies as well as international trade regulations.