A massage assembly (20) wherein a massage unit (40) comprising a therapeutic member (50) for massaging the body of the user by a kneading and/or tapping movement is reciprocatingly moved between a pair of frames (22) (23) and which comprises a motion converting mechanism for converting the reciprocating movement of the massage unit (40) to the kneading and/or tapping movement of the therapeutic member (50). The massage assembly (20) is incorporated in a backrest (16) of a chair (12) or a bed to provide a massage machine (10) of the invention.