When the temperature of a powder compact is raised, heat diffuses inwards from the surface. If the compact is under pressure (as it is during HIPing), the surface layers start to densify, increasing the local thermal conductivity. Under certain conditions a densification front then propagates into the powder, and this leads to changes of shape of the compact, which is no longer identical to the preform shape. The conditions which lead to non-uniform densification are analyzed and the consequences are discussed, and compared with experiments