A pressure bandage (100) for applying pressure to a target site comprising (i) a backing layer (102) with a coating of a pressure-sensitive adhesive on a first major surface of the backing layer, and (ii) a snap-bucklable member (104) coupled to the backing layer an capable of snap-buckling from a concave to a convex configuration after the bandage has been adhesively applied over the target site so as to apply continuous pressure to the target site so long as the bandage is worn. The pressure bandage may be positioned over a bleeding target site to apply pressure to the target site and reduce bleeding.