The stability of compression members is typically assessed through buckling curves, which include the influence of initial geometric imperfections and residual stresses. Alternatively, the capacity may be obtained more directly by carrying out either an elastic or an in elastic second order analysis using equivalent bow imperfections that account for both geometric imperfections and residual stresses. For design by second order elastic analysis, following the recommendations of EN 1993-1-1, the magnitudes of the equivalent bow imperfections can either be back-calculated for a given member to provide the same result as would be obtained from the member buckling curves or can be taken more simply as a fixed proportion of the member length. In both cases, a subsequent M–N (bending + axial) cross-section check is also required, which can be either linear elastic or linear plastic. For design by second order inelastic analysis, also referred to as design by geometrically and materially nonlinear analysis with imperfections (GMNIA)there are currently no suitable recommendations for the magnitudes of equivalent bow imperfections and, as demonstrated herein, it is not generally appropriate to use equivalent bow imperfections developed on the basis of elastic analysis. Equivalent bow imperfections suitable for use in design by second order inelastic analysis are therefore establishedin the present paper.The equivalent bow imperfections are calibrated against benchmark FE results, generated using geometrically and materially nonlinear analysis with geometric imperfections of L/1000(L being the member length)and residual stresses. Based on the resultsobtained, an equivalent bow imperfection amplitude e0= L/150 ( being the traditional imperfection factor set out in EC3), isproposedfor both steel and stainless steel elements and shown to yield accurate results.The reliability of the proposed approach is assessed, using the first order reliability method set out in EN 1990, against the benchmark FE ultimate loads, where it isshown that partial safety factors of 1.0 for steel and 1.1 for stainless steel canbe adopted.