Abstract
We consider the problem corresponding to the torsion of a cylindrical beam which incorporates the effects of material microstructure. The beam is modelled using micropolar or Cosserat elasticity and the boundary integral equation method is used to solve the corresponding boundary value problem. The exact solution is found in the form of an integral potential which is then approximated numerically using a Fourier series based on the corresponding singular solutions of the governing equations. We give an example, which demonstrates the effectiveness of the numerical method.