Residual stresses in cold-formed members may play a significant role in determining their behaviour and strength, and have traditionally been obtained by laboratory measurements. This paper presents the results of research which forms part of a larger study on the theoretical predictions 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 sections. In this paper, a 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. To facilitate its application in subsequent finite element simulation of the cold-forming process, the prediction of equivalent plastic strains is also addressed in this solution. 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 development process of residual stresses and the effects of coiling curvature and yield stress on the final residual stresses. © 2004 Elsevier Ltd. All rights reserved.