Purpose. The article is aimed to perform a structural analysis of the main and auxiliary mechanisms of tube straightening machines, to identify structural and local redundant links in the mechanism schemes, and to offer recommendations on their rational design. Methodology. The solution is realized by means of the theory of mechanisms and machines using structural analysis of the mechanisms of tube straightening machines based on the universal structural theory of O.G. Ozol. Findings. The extended principle of the machine’s mechanism formation, which provides inclusion to the mechanism not only невільних solid bodies, but also the deformed bodies, allows us to consider the structure of machines for pressure processing of metals, taking into account the plastically deformed workpiece. Therefore, such machines include in their composition a deformed workpiece as an integral part of the machine mechanism, whose deformation and addition of certain geometric parameters to it is the reason the tube straightener was created for. Defects in the machine structure are determined by the local and structural redundant links included in the kinematic chains of the mechanisms, which transform the mechanism into a statically undetermined system. Movement of the mechanism with defects in the structure is possible in the presence of gaps or due to deformation of the links. The main mechanism of the tube straightening machine is a mechanism of variable structure, therefore, an analysis for its two states is carried out: before the tube is caught by the rollers and during its straightening. For calculation of the number of mobilities of the outer «roll – tube» pair, it was taken into consideration that most of the coordinates are overlaid with non-retentive links, which contain a fractional number of constraints. Fifteen redundant links were identified in the main mechanism and their amount in the auxiliary mechanisms of the tube straightening machine was established. Originality. The structural analysis of tube straightening machines with the search for redundant links was never performed. A structural analysis of the mechanisms of cross roll tube straightening machine was performed for the first time, taking into account the presence of external fractional links that are superimposed in the «roll-tube» pairs. Practical value. The practical recommendations for eliminating the harmful redundant links that were found in the structural analysis of the main and auxiliary mechanisms of the tube straightening machine were developed.