Cold-formed steel hollow sections are usually produced by first cold bending an uncoiled steel sheet transversely into a circular shape and then cold rolling the circular tube into a desired cross-sectional shape, in which the operation for forming the initial circular shape into the final cross-sectional shape is referred to as shaping. This paper is concerned with co-existent residual stresses and strain hardening of materials in both cold-formed steel circular and elliptical hollow sections. The paper presents a finite element-based method for the prediction of residual stresses and equivalent plastic strains in these cold-formed steel hollow sections. In this method, the residual stresses and equivalent plastic strains that arise from the coiling, uncoiling and transverse bending of the steel sheet into the circular shape are predicted analytically, and specified as the initial state for a subsequent finite element simulation of the shaping operation. The method provides residual stress distributions over the cross section as well as across the thickness, which are too complicated to be precisely measured in laboratory. The validity and accuracy of the method are demonstrated by comparing its predictions with existing laboratory measurements of residual stresses. The method presented in the paper can be used for examining the influence of different forming parameters on the co-existent residual stresses and strain hardening of materials which can subsequently affect the member behaviour of hollow sections