The evolution of the Arctic polar vortex during observed major midwinter stratospheric sudden warmings (SSWs) is investigated for the period 1957–2002, using 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) Ertel’s potential vorticity (PV) and temperature fields. Timelag composites of vertically weighted PV, calculated relative to the SSW onset time, are derived for both vortex-displacement SSWs and vortex-splitting SSWs, by averaging over the 15 recorded displacement and 13 splitting events. The evolving vertical structure of the polar vortex during a typical SSW of each type is clearly illustrated by plotting an isosurface of the composite PV field, and is shown to be very close to that observed during representative individual events. Results are verified by comparison with an elliptical diagnostic vortex moment technique. For both types of SSW, little variation is found between individual events in the orientation of the developing vortex relative to the underlying topography; that is, the location of the vortex during SSWs of each type is largely fixed in relation to the earth’s surface. During each type of SSW, the vortex is found to have a distinctive vertical structure. Vortex-splitting events are typically barotropic, with the vortex split occurring near simultaneously over a large altitude range (20–40 km). In the majority of cases, of the two daughter vortices formed, it is the ‘‘Siberian’’ vortex that dominates over its ‘‘Canadian’’ counterpart. In contrast, displacement events are characterized by a very clear baroclinic structure; the vortex tilts significantly westward with height, so that the top and bottom of the vortex are separated by nearly 1808 longitude before the upper vortex is sheared away and destroyed.