Apparatus (60) for supporting a subject (2) in an inverted state comprises a ground engaging plinth (8) and a support platform (12) pivotally coupled to the plinth (8) about a first pivot axis (15) so that the support platform (12) is pivotal between a first state with a subject (2) in a supine state on the support platform (12) and a second state with the subject (2) inverted on the support platform (12). The subject is supported in the inverted state on the support platform (12) by shoulder engaging elements (24), and is secured to the support platform (12) by a torso strap (35). A foot engageable element (77) connected to a weight carrying bar (84) through connecting members (79,82) extending through an elongated slot (80) in the support platform (12) allows leg and abdominal muscles to be exercised by urging the foot engageable element (77) in the direction of the arrow A against weights (85) carried on the weight carrying bar (84). A carrier element (81) slideable on a guide bar (83) guides the foot engageable element (77). Handgrips (86) are connected by steel cables (87) around pulleys (88,89,90,91) to the weight carrying bar (84) for facilitating exercising of arm, shoulder, chest and back muscles.