A comprehensive investigation into the behaviour of structural stainless steel members under concentrated transverse loading is presented in this paper. A total of 34 member tests and over 500 finite element simulations have been performed covering three types of concentrated transverse loading – internal one‐flange, internal two‐flange and end one‐flange loading, three stainless steel grades – austenitic, duplex and ferritic and key influential parameters such as bearing length, web slenderness and beam span. The results have shown that existing design recommendations are conservative and that there is considerable scope for the development of more economical design guidance. New design equations are proposed that offer 10% to 20% improvements in capacity predictions over the current design formulae in EN 1993‐1‐4. These proposed design equations are to be included in the next revision of the European standards. An alternative design approach based on numerically generated reference loads – i.e. the plastic collapse and elastic buckling loads – in conjunction with strength curves, has also been proposed. This advanced FE‐based design approach allows the extension of the design scope to non‐standard cases, such as webs with partial depth stiffeners and members with web holes. The reliability of both design approaches has been successfully verified by statistical analysis.