•Cold-formed stainless steel RHS undergoing combined bending and web crippling was studied.•34 tests were conducted on specimens of lean-duplex and ferritic stainless steel grades.•Parametric studies of 312 specimens were performed.•Current combined bending and web crippling design provisions are shown to be conservative.•Improved design rules are suggested in this study. The behaviour and resistances of cold-formed stainless steel rectangular hollow section (RHS) members undergoing combined bending and web crippling were studied based upon experimental and numerical investigations. A test program consists of 4 pure bending tests, 7 pure web crippling tests and 23 web crippling-bending interaction tests was conducted. The RHS specimens were cold-rolled from lean-duplex and ferritic stainless steel sheets. Numerical models were built and validated against the test results. Upon validation, parametric studies comprised of 312 finite element analyses were undertaken. The obtained test and numerical results were compared with nominal resistances predicted from the American, Australian/New Zealand and European design standards for stainless steel structures. Moreover, the provisions in the North American Specification for cold-formed steel members were also evaluated. The comparison results indicate that the codified design provisions are generally safe to use for design of cold-formed stainless steel RHS members undergoing combined bending and web crippling, among which the European provision yields overly-conservative predictions. The codified web crippling-bending interaction curves can be applied for designing the stainless steel RHS members undergoing combined bending and web crippling, whilst improved predictions could be achieved by employing recently proposed bending and web crippling design rules.