The manufacturing process of cold-formed steel members induces cold work which has a significant effect on their structural performance. In order to assess this cold-working effect, residual stresses and equivalent plastic strains need to be quantified. A finite element-based method was recently proposed by the authors for predicting the coexistent residual stresses and plastic strains in cold-formed steel hollow sections. In the present study, this finite element-based method was employed to carry out a parametric study in order to generate numerical data of the residual stresses and coexistent equivalent plastic strains in cold-formed steel elliptical hollow sections (EHS) for a wide range of steel grades (including both normal grade steels and high strength steels) and section sizes. By analyzing these numerical data, simplified models for residual stresses and coexistent equivalent plastic strains in cold-formed steel EHS are proposed. The simplified models can be employed to define the initial states of cold-formed steel EHS members in a nonlinear finite element analysis for their structural performance, and thus can be used to examine the cold-working effect on the member behavior in future studies.