<p>Cross-sectional warping and distortion effects may play a significant role in the axial, bending, and torsional modes of rods, especially for very large deformations. This paper investigates the ability of higher-order beam elements based on the Absolute Nodal Coordinate Formulation (ANCF) to accurately describe the mechanical behavior of solid rods with complex cross-sections, in which the transverse parameters of the position vector are constructed using the Taylor-like polynomials. In order to consider the coupling of deformations, the nonlinear strain–displacement relations are established by the continuum mechanics theory. Furthermore, a numerical quadrature scheme for different cross-section configurations is presented. By comparison to the finite solid element in common software ABAQUS, the results demonstrate that the second-order and fourth-order ANCF beam elements can achieve sufficient accuracy for the rod cross-sectional deformations during the bending and torsion process, respectively. The work provides a basis for element choice in static and dynamic simulations of rod-type structures.</p>