The Swift effect, i.e. the length changes during torsion of solid bars with axial freedom of deformation is analysed theoretically for polycrystalline copper. In the simulations, the bar is divided into 5 tubes and in each tube the texture development is simulated with the help of the Taylor viscoplastic polycrystal model. The distribution of the hydrostatic stress is obtained from the equilibrium equation and the zero axial force requirement is satisfied with the help of an iterative scheme. The simulations reproduce faithfully the observed axial deformation and texture development. A second technique, based on the minimum plastic power is also applied to predict the length changes and textures. This technique leads to results which are nearly equivalent to the results obtained from the technique based on the equilibrium equation.