Abstract: A disposable cover for a pet bed or resting surface comprises an outer layer having a perimeter; an elastic member located about the perimeter for fixing the cover with respect to the pet bed/resting surface; an inner layer for contact with the resting surface; and an intermediate layer which includes odor-absorbent material. A method of eliminating pet odor comprises providing a resting surface for a pet; covering the resting surface with a disposable odor-absorbent cover; and fixing the disposable cover to the resting surface with the attachment member.