AbstractThe development and implementation of a four‐noded quadrilateral element for the analysis of the axisymmetric‐torsion problem is presented in the context of the mixed‐enhanced method. The deformation gradient is developed from two sets of element interpolants, of which one may be explicitly obtained resulting in only two undetermined enhanced parameters needed for the satisfaction of the near incompressible limit. The resulting element arrays yield proper rank with standard 2×2 quadrature. The introduction of a three‐field variation statement for the problem along with the interpolations for the stress and deformation gradient render a variational stress recovery permissible. Several numerical examples are explored in the setting of finite kinematics with physically non‐linear material properties to further induce coupling between the radial and axial displacement and the longitudinal rotation. Copyright © 2004 John Wiley & Sons, Ltd.