An apparatus for promoting the clotting of blood and controlling bleeding comprises a receptacle for retaining molecular sieve material in particulate form therein. A pad for controlling bleeding comprises a mesh structure and a rigid or semi-rigid support attached to the mesh structure to facilitate the application of pressure to the pad and the wound. A bandage applicable to a bleeding wound comprises a mesh structure and a flexible substrate attached to the mesh structure, the substrate being a cloth or plastic member that may be adhesively attached to cover a wound. In any embodiment, at least a portion of the receptacle or mesh structure is defined by a mesh having openings therein, and at least a portion of the particulate molecular sieve material is in direct contact with blood.