A pad of elastomeric material having a softness of no more than about durometer 50 Shore 00. The pad may carry adhesive and/or a housing for adhering the pad to a surface, either directly or indirectly through an envelope which surrounds the pad and carries the adhesive. Such a pad exhibits hemostatic and leak prevention properties against needle puncture holes in the skin or the wall of a hollow medical device. Particularly, hemostasis may be prevented with low pressure application of the pad to the skin. The pad may be previously applied to the skin of the patient or a wall of a medical device such as tubing or a solution bag, and the needle may then penetrate both the pad and the skin or medical device wall, to make a resealable puncture with leakage reduction and hemostasis when the needle is withdrawn.