In contrast to straight bars, elastic bars with initial twist exhibit coupling between tension and torsion. The coupling is examined for pretwisted bars composed of homogeneous isotropic material under the assumption that each section undergoes the same deformation. The expressions for the axial force and torsional moment are transformed by use of the governing equations and boundary conditions to forms that are particularly useful for rods with small amounts of pretwist. The elliptical section with center on the axis of pretwist and the off-centered circular section are treated in order to illustrate the coupling between extension and torsion caused by the initial twist.