Multifiber beam models have proved to be an efficient numerical tool to simulate the behavior of slender structural elements subject to normal stresses. However, the response of these models in the case of shear dominating loads lacks in accuracy. The present study addresses this problem by introducing torsional warping in the kinematics of multifiber beam elements, with nonlinear constitutive behavior. Both theoretical and numerical formulations are developed to compute the warping function of an arbitrary-shaped composite cross-section. The resulting warping profile is compared with the actual axial displacement profile in a 3D simulation of a beam under torsion. The warping kinematics is then implemented in a Timoshenko multifiber beam element. Global torsional response of a concrete beam in torsion is computed using a 3D damage law. A comparison of torque-twist curves obtained with enhanced and classical beam elements to experimental curves highlights the importance of including warping in the model, for both the initial stiffness and the torsional strength responses. The improvement is further ascertained by analyzing the damage patterns in the beam crosssections.