A limp string loaded only by its own weight has a nonlinear differential equation which may be integrated as two first-order equations with arc length parameter. If bending stiffness is also included, such a procedure fails since the order of the differential equation increases by two. In this paper it is shown that relatively small stiffness causes an effect only in boundary regions near the end supports and that the deviation from the catenary can be found as a rapidly converging series. The bending stress and the correction to the sag and length can be found from these correction terms. This result is used to find the bending stress caused in cables by vertical suspenders and in drill pipe by end fixity or moment.