Despite significant advances in metallurgy and the potential to create high and very high-strength steel, all international specifications for steel design provided little information about the limits of slenderness for high-strength steel sections (HSSs) and didn’t give anything about the design of very high-strength steel sections (VHSSs). The American structural steel design specification covers circular hollow sections (CHS) of steel grades up to S690, while it isn't in ANSI/AISC 360-16 and ASTM A514/A514M. Euro code EN 1993-1-1 can be applicable only to steel grades up to S460. EN 1993-1-3 and EN 1993-1-12 contain supplementary rules for cold-formed members and HSS (S460- S700), respectively. Though ductility requirements for (HSS) are specifically established in EN 1993-1-12, it is largely a continuation of the normal-strength-steel design procedures standardized in EN 1993-1-1, where (HSSs) are largely treated as normal-strength steels in these rules, and the same design approaches are used. The behavior of high and very high-strength steel circular hollow sections under axial compression load is studied in this research. A total of 16 nonlinear finite-element (FE) models were generated to replicate stub column tests that were experimentally tested by others in previous research. Hence, a parametric study is conducted using forty FE models developed to investigate the local buckling behavior under various slenderness ratios comprehensively. The developed models cover slenderness ratios ranging from 20 to 1226 and steel grades S460 and S1100 with yield stress equal 460 MPa and 1152 MPa, respectively. The FE results were combined with 105 previously collected experimental results to assess the applicability of existing codified design methodologies in the Euro code and the North American codes of cold-formed CHS. Based on the results of this study, new cross-sectional slenderness limits and new design equations for more efficient simple designs were presented for high and very-high strength steel circular hollow sections and Compared with the results of experimental tests and FE models.