An apparatus and a relative method for measuring straightness errors of elongated-shape elements, such as bars, tubes and the like is presented. The measuring apparatus includes a supporting system for a bar, a first detecting system having one or more first sensors to detect the development of the longitudinal axis of the bar, and a central control unit. The measuring apparatus further includes a second detecting system provided with a plurality of second sensors to detect the forces the bar applies to the supporting system and acquiring means to acquire at least one physical parameter of the bar under measuring. The central control unit includes at least one data acquiring and processing module to acquire and process the data detected by said first and second detecting systems and acquired by said acquiring means, in order to determine the possible straightness error of the bar.