A boundary element (B.E.) solution for the Saint‐Venant torsion problem for composite cylindrical bars of arbitrary cross section is presented. The composite bar consists of a cylindrical matrix material surrounding a finite number of inclusions with different shear moduli firmly bonded to it. The problem is formulated in terms of the torsion function, which is established by solving a Neumann‐type boundary value problem. Moreover, the torsional rigidity of the composite cross section and the shear stress components are evaluated. Several numerical examples are worked out and the results are compared with those available from analytical or other numerical solutions. The case of the homogeneous cross section with or without holes is obtained as a special case. The efficiency of the B.E. method is also demonstrated and examined.