Thin-walled beams exhibit a nonlinear response to bending moments due to the progressive flattening of the crosssection, a behavior commonly referred to as the Brazier effect. Most approaches to model this effect are limited to either circular cross-sections or to cross-sections made of isotropic materials. This article proposes an efficient two-step method of predicting the nonlinear collapse of thin-walled cross-sections of arbitrary geometry with isotropic and orthotropic materials. The procedure relies on representing the cross-section by two-dimensional nonlinear corotating beam elements with imposed in-plane loads proportional to the curvature, combined with a finite strip buckling analysis based on the deformed cross-section. By comparison with existing analytical and numerical modeling approaches, it is demonstrated that the present method can capture the cross-section flattening and critical moment for buckling of thin-walled structures commonly found in the industry.