The invention relates to a shoulder press machine having a seat, a backrest and fixed framework at the top of which a carriage is mounted. The carriage has a pair of downwardly and forwardly extending, diverging lever arms which are tied together and moved upwardly and downwardly along a major horizontal axis mounted to the framework behind the backrest and a minor horizontal axis offset behind and parallel to the major horizontal axis. As the lever arms are moved together upwardly, they are simultaneously swung inwardly about a pair of parallel, angular pivot axes, the swinging motion being transferred via a pair of transfer links to pivot a pair of sleeves about the minor horizontal axis. As a result of these linkages, a shoulder press machine is provided in which an exerciser's hands rotate or supinate naturally through approximately 20.degree.-30.degree. as the lever arms are pushed upwardly. The inventive machine much more easily accommodates the natural musculoskeletal make-up of the human body without stress to the shoulder joints.