A numerical investigation of cold-formed high strength stainless steel square and rectangular hollow sections in compression has been presented in this paper.A non-linear finite element model that includes geometric and material non-linearities was developed and verified against experimental results. The model was then used for an extensive parametric study to investigate the interaction effects of constituent plate elements on Class 3 slenderness limit and section capacities of cold-formed high strength stainless steel square and rectangular hollow sections in compression. It is shown that the interaction effects of constituent plate elements on cross-section response are quite obvious particularly for slender sections. The design provisions on Class 3 slenderness limit in the EC3 Code and proposed by Gardner and Theofanous are suitable for square hollow sections, but not for rectangular hollow sections since they do not take into consideration of interaction effects of constituent plate element. Therefore, a new Class 3 slenderness limit is proposed in this study, which carefully considers the interaction effects of the constituent plate elements.