The direct analysis method (DAM), featuring second order elastic analysis with two stiffness reduction factors - τb and τg, is the primary means of stability design for steel structures in AISC 360 and AISI S100. The equivalent provisions for stainless steel structures, which are due to be incorporated into the upcoming AISC 370 and ASCE-8 Specifications are developed herein. Stainless steel exhibits a rounded stress-strain response, typically described by the Ramberg-Osgood formulation. The slope of this function (i.e. the tangent modulus), adjusted to consider the influence of residual stresses, is used to define the stiffness reduction factor τb at a given axial load level to be applied to members in compression to allow for the adverse influence of the spread of plasticity and residual stresses. The dependency of the degree of stiffness reduction on the roundedness of the stress-strain curve, which varies between the different grades of stainless steel is also directly captured through the strain hardening exponent n that features in the Ramberg–Osgood formulation. Values of 0.7 for AISC 370 and 0.9 for ASCE-8 are proposed for the general stiffness reduction factor τg to be applied to all member stiffnesses to account for the development and spread of plasticity, and to ensure a suitable reduction in stiffness for slender members with low axial load levels. The different τg values between the two specifications is required to reflect the different buckling curves and axial-bending interaction expressions employed. The accuracy of the proposed method for the design of stainless steel members and frames is assessed through comparisons with benchmark shell finite element results. Comparisons are also made against the new provisions in AISC for design by second order inelastic analysis. The reliability of the design proposals is demonstrated through statistical analyses, where it is shown that a resistance factor ϕ of 0.9 can be adopted.