An advanced finite element (FE)-based method has been recently proposed to determine the complete fields of both residual stresses and plastic strains in cold-formed tubular sections, and validated against the existing test results. By using this validated method, a comprehensive parametric study for plastic strains and residual stresses in cold-formed stainless steel (CFSS) elliptical hollow sections (EHS) was conducted; covering a wide range of stainless steel alloys, aspect ratios, cross-section dimensions and slenderness. By analyzing these FE data, the predictive models and simplified distributions of both the residual stresses and equivalent plastic strains in CFSS EHS, are proposed in present study; which are expressed in terms of the key forming parameters. In these models, residual stresses across the thickness were decomposed into a constant membrane component plus a stress-box bending component, while equivalent plastic strains were simplified with a multi-linear variation across the thickness. It was found that the normalized magnitudes of both the residual stresses and equivalent plastic strains generally increased with the increasing cross-section aspect ratios, but decreased with the increasing normalized cross-section slenderness values. The type of stainless steel alloys had a negligible effect on both the normalized residual stresses and normalized plastic strains. Finally, the predictive models were adopted to define the initial states of CFSS EHS stub columns for investigating the cold-work effect on the column behavior. It can be concluded that the cold work can significantly enhance the ultimate capacities of the columns.