This paper presents the results of recent research which forms part of a larger study on the theoretical prediction of residual stresses in cold-formed sections. The paper is concerned with residual stresses that arise from the coiling and uncoiling process experienced by steel sheets before they are cold-formed into shapes. In this paper, an analytical closed-form solution is presented for these residual stresses, in which the coiling and uncoiling process is modelled as an elastic-plastic plane strain pure bending problem with the steel assumed to obey the von Mises yield criterion and the Prandtl-Reuss flow rule. The accuracy of the solution is demonstrated by comparing its predictions with those from a finite element simulation. Numerical results from the analytical solution are also presented to illustrate the effects of coiling curvature and yield strength on the residual stresses.