The method of enhanced assumed strains (EAS) is a popular tool for avoiding locking phenomena, e.g., a remedy for shear locking in plane elasticity. We consider bending-dominated problems on thin bodies which can be treated as beams and prove that the degree of approximation of the EAS method is at least as good as that of a beam model. The hypercircle method is combined with arguments of nonconforming methods. Key words. 2D-elasticity, enhanced strain method, shear locking, nonconforming element AMS subject classifications. 65N30