Although dynamic stress changes associated with the passage of seismic waves are thought to trigger earthquakes at great distances, more than 60 per cent of all aftershocks appear to be triggered by static stress changes within two rupture lengths of a mainshock. The observed distribution of aftershocks may thus be used to infer details of mainshock rupture geometry. Aftershocks following large mid-continental earthquakes, where background stressing rates are low, are known to persist for centuries, and models based on rate-and-state friction laws provide theoretical support for this inference. Most past studies of the New Madrid earthquake sequence have indeed assumed ongoing microseismicity to be a continuing aftershock sequence. Here we use instrumentally recorded aftershock locations and models of elastic stress change to develop a kinematically consistent rupture scenario for three of the four largest earthquakes of the 1811-1812 New Madrid sequence. Our results suggest that these three events occurred on two contiguous faults, producing lobes of increased stress near fault intersections and end points, in areas where present-day microearthquakes have been hitherto interpreted as evidence of primary mainshock rupture. We infer that the remaining New Madrid mainshock may have occurred more than 200 km north of this region in the Wabash Valley of southern Indiana and Illinois-an area that contains abundant modern microseismicity, and where substantial liquefaction was documented by historic accounts. Our results suggest that future large midplate earthquake sequences may extend over a much broader region than previously suspected.