AbstractIt is well known that with the assumption of constant strain elements, the Galerkin approach yields a numerical solution of the equilibrium equations of a beam with shear deformation which exhibits the unphysical feature of shear locking. Here, it is shown that the numerical solution that is based on the theory of a Cosserat point converges to the exact solution of the beam theory even when the kinematics are consistent with the constant strain assumption and the beam thickness approaches zero. The main difference between these two numerical approaches is the way they each determine the constitutive equations (or stiffnesses) of the elements. The Galerkin approach determines the stiffnesses of each element by integrating the constitutive equations for the beam assuming that the kinematic approximation is valid pointwise. In contrast, the constitutive equations of the Cosserat point are related to derivatives of a strain energy function and the constitutive constants are determined using a physical approach which matches the responses to simple shear and pure bending. The results indicate that the Cosserat approach takes full advantage of the reduced number of degrees of freedom used to describe the beam. Copyright © 2001 John Wiley & Sons, Ltd.