A gripping machine for an article includes a machine frame, first and second drive means associated with the machine frame, a support platform of the article, movable with respect to the machine frame by the first drive means along a direction of displacement, and holding members, arranged about the direction of displacement to delimit therebetween a gripping plane or space of the article, at least one holding member being movable radially by the second drive means between a holding configuration and a release configuration of the article, and vice versa. Electronic control means control the first drive means so that the support platform is located at one or more predefined axial positions and the second drive means so that, in the holding configuration, at least one holding member is moved continuously towards the article to actively clamp the article.