The subject invention pertains to materials and methods for processing tissue to produce a natural, acellular replacement tissue that is immunocompatible with a recipient. According to the subject invention, harvested tissue is subjected to wash solutions wherein only amphoteric detergent(s) are used (e.g., anionic detergents are excluded). Following extraction by amphoteric detergent(s), the tissue is washed with a buffer system to facilitate the clearance of cellular components and detergent. In one embodiment, the subject invention pertains to a replacement tissue that is a nerve graft that supports axonal regeneration, guides axons toward the distal nerve end and/or is immunologically tolerated. Preferably, the nerve graft retains essential extracellular matrix scaffolding as well as biological components that promote nerve regeneration through the nerve graft.