A mechanical pressing machine includes a slider mounted on an input shaft at a location below a cam, and a sliding block and a balance weight mounted at locations above the cam. A first cam follower rotatably carried on the slider abuts against a lower surface of the cam and is biased by a spring member toward the lower surface. A second cam follower rotatably carried on a sliding block abuts against an upper surface of the cam and is biased by spring members toward the upper surface. When the cam is rotated together with the input shaft, the slider effects vertical sliding movement through the first cam follower, and the sliding block and the balance weight effect vertical sliding movement in a direction opposite from the direction of movement of the slider through the second cam follower.