A method of waterproofing or damp proofing a protected member having a surface with a sulfur-extended elastomer asphalt binder composition uses a sulfur-extended elastomer asphalt binder composition that includes elemental sulfur, an elastomer and an asphalt binder. The method includes the steps of combining the elastomer with the asphalt binder maintained at an elastomer mixing temperature such that an intermediate asphalt binder mixture forms, and combining elemental sulfur with the intermediate asphalt binder maintained at a sulfur mixing temperature such that the sulfur-extended elastomer asphalt binder composition forms. The method also includes the step of applying the sulfur-extended elastomer asphalt binder composition to the surface of the protected member such that the sulfur-extended elastomer asphalt binder composition contacts, adheres to and forms a layer upon the surface of the protected member. The asphalt binder composition is applied at a temperature no greater than 145° C.