An approximate theory is developed to determine the compound stress state existing in helical wires of a cable bent through a planar circular arc. Approximations arise through the treatment of the frictional interface between layers of wires. Furthermore, all materials are assumed to be linearly elastic. The model does, however, recognize geometric nonlinearities in terms of the strain-displacement relations for wire elongation and curvature. The theory presented reveals the nature of axial, bending and torsional shearing stresses produced in round helical wires. Comparisons with experimental data show reasonable agreement.