The nonlinear finite element （FE） models of stainless steel I-section and rectangular hollow section （RHS） stub columns were established to analyze the local stability of the novel high-strength QN1803 stainless steel axial compression members after elevated temperature. Parametric analysis was carried out to analyze the effects of residual stress， initial local imperfections， and elevated temperature conditions on the local stability and bearing capacity of the members. The results show that for RHS and “non-slender” plate of I-section members with non-dimensional plate slenderness ratio less than 1.0， residual stress has little effect on bearing capacity； for “slender” I-section members， residual stress reduces the section bearing capacity， and the reduction decreases with the increasing temperature. In addition， with the increase of temperature， the limit value of non-dimensional plate slenderness ratio at which the initial local imperfections have a significant impact on the bearing capacity of stainless steel I-shaped members becomes larger， and the influence on the bearing capacity of stainless steel RHS members gradually becomes smaller. Finally， an assessment of the applicability of the design provisions for stainless steel structures at room temperature， as given in the European code EN 1993-1-4 and ASCE/SEI 8-02， together with the Chinese specification CECS 410： 2015， to the design of stainless steel stub columns after elevated temperature is subsequently performed through comparisons against the obtained numerical data. It is found that the existing design codes at room temperature are not fully applicable to the design and prediction of stainless steel stub columns after elevated temperature. And there were still unreasonable aspects in the post-fire design in the existing research. It is suggested to further optimize the evaluation method of local stability of stainless steel members after elevated temperature.