An analytical model is developed to study the extension-bending-torsion coupling behavior of an initially twisted elastic beam with an irregular cross-section. The determination of the complete displacement field requires solving a coupled two dimensional boundary value problem in a curvilinear coordinate system for the local deformations in the section plane and warping out of the section plane. The principle of minimum potential energy is applied to a discretized representation of the cross-section (Ritz method) to calculate solutions to this problem. Numerical results illustrate the pronounced effects pretwist, initial twist axis location, and in-plane deformation have on the behavior of solid and single and multi-celled sections, including airfoil sections.