The n-type and p-type leg structure of any conventional thermoelectric module are in the form of filled rectangular shape which are placed next to the each other (see graphical abstract). In this paper, hollow cylindrical configuration is investigated as a novel leg structure for thermoelectric module in which the n-type and p-type legs are placed co-axial inside each other. A validated 3D numerical simulation was employed to investigate the proposed structure from thermal, economic, exergetic and mechanical viewpoints. The cylindrical ring-shape co-axial configuration can be made in different azimuthal angle, slant angle and width ratio all of which are probed in this research under different boundary conditions. The ring shape structure is able to reduce the thermal-stresses level without the reduction of thermal efficiency. Results indicate that the increment of hot side temperature can improve the output power and conversion efficiency of the cylindrical thermoelectric generator (CTEG) device but reduces the mechanical reliability of the system. It addition, with increment of slant angle of thermoelectric legs, the maximum Von Mises stress in the legs increases and power output of the CTEG is improved. The increase of the width ratio leads to the improvement of the output power and reduction of conversion and exergy efficiencies. Moreover, it is proved that the azimuthal angle of CTEG device has minor impact on the conversion and exergy efficiencies. It is found that the Von Mises stress attains the peak values in the contact regions between wielding layers and hot sides of the legs.