This paper describes a numerical investigation into the out-of-plane buckling behavior of freestanding roller bent steel arches. As roller bent arches have structural imperfections which differ considerably from those of hot-rolled or welded sections, specific attention is paid to their inclusion in the numerical model. Sensitivity analyses are performed to assess the influence of the imperfections due to roller bending on the out-of-plane buckling response. The accuracy of the finite element model is checked by comparing the results with earlier performed experiments as presented in a related paper. The finite element model is able to replicate the structural behavior displayed by the experiments with good accuracy. A database is created with elastic– plastic buckling loads for a large number of freestanding roller bent arches. The numerical data is analyzed and presented in a so-called imperfection parameter diagram from which imperfection parameter curves are derived. The imperfection parameter curves are substituted into the European column curve formulation, leaving the original column curve formulation unaffected but extending its applicability to the out-of-plane buckling response of roller bent arches. The column curve with proposed imperfection parameter expressions can be used to check the out-of-plane buckling response of a roller bent steel arch with known non-dimensional slenderness. © 2012 Elsevier Ltd. All rights reserved.