A method of making an external breast prosthesis by forming an elastomeric skin in the form of a human breast surrounding an inner material such as a silicone gel or hydrogel. The elastomeric skin can be formed from a front skin and a rear skin, and the skins can be made of a soft styrenic elastomer having attributes similar to a gel. At least the front skin is formed by mixing together a polymer, a plasticizing oil and at least one non-volatile additive to form a mixture, heating the mixture, forming the mixture into a front elastomeric skin, and cooling the mixture thereby allowing the non-volatile additive to precipitate to the outer surface of the outer skin to form a cratered outer surface that is substantially soft to the touch and that tends to maintain the skin in a pliable yet pre-defined shape.