The power transmission shafts, steering rods and power screws are bars subjected to axial twisting moment [causing twist (torsion)] and other loads. The torsion of a circular bar (cross-sections do not warp) is developed and applied to helical spring, flange coupling and rivetted bracket. The torsion of a cylinder of arbitrary cross-section made of isotropic material involves warping of the cross-sections. The solution is presented in terms of Prandtl’s stress function. Solutions for bars with thin rectangular section, thin open sections, thin-walled closed single-cell and multiple-cell sections are presented. The limiting torque for bars of elastic perfectly-plastic material is discussed.