The structural behaviour and design of stainless steel hollow sections in fire, including stainless steel (i) circular hollow sections (CHS), (ii) elliptical hollow sections (EHS), (iii) square hollow sections (SHS) and (iv) rectangular hollow sections (RHS), are explored in this paper. Shell finite element models of stainless steel CHS, EHS, SHS and RHS able to replicate their structural response at elevated temperatures are created. Numerical parametric studies are performed on cold‐formed and hot‐rolled austenitic, duplex and ferritic stainless steel CHS, EHS, SHS and RHS subjected to (i) pure compression, (ii) pure bending, (iii) combined axial compression and bending and (iv) combined bending and shear in fire, covering different cross‐section slendernesses and elevated temperature levels. Calibrated against the benchmark structural performance data obtained from the numerical parametric studies, the new design proposals for predicting the ultimate resistances of stainless steel CHS, EHS, SHS and RHS in fire put forward in Quan and Kucukler [1,2] are set out. It is demonstrated that relative to the design recommendations provided in the European structural steel fire design standard EN 1993‐1‐2, the proposed cross‐section design methods provide more accurate and safe‐sided ultimate resistance predictions for stainless steel CHS, EHS, SHS and RHS at elevated temperatures.