Steel cables play an important role in many offshore applications. In many cases, an understanding of the magnitude and pattern of bending stresses in the individual component wires of a bent strand is essential for minimizing the risk of their failure under operating conditions. Following previously reported experimental observations, a theoretical model is proposed for obtaining the magnitude of wire bending stresses in a multi-layered and axially preloaded spiral strand fixed at one end and subsequently bent to a constant radius of curvature. The individual wire bending stresses are shown to be composed of two components. The first component is the axial stress generated in the wires due to interwire/interlayer shear interactions between the wires in a bent cable, and the second component is associated with the wires bending about their own axes. Using the theoretical model, which includes the effects of interwire friction, parametric studies on a number of realistic helical strands with widely different cable (and wire) diameters and lay angles subjected to a range of practical mean axial loads, and subsequently bent to a range of radii of curvature with one end of the cable fixed against rotation, have been carried out. It is shown that for most practical applications, the axial component of wire stresses due to friction is much greater than the second component of bending stresses associated with the individual wires bending about their own axes.