First, a screw dislocation in an infinite medium is analyzed by the theory of nonlocal elasticity. Then, the nonlocal elastic interaction energy between a screw dislocation and a point defect caused by an interstitial carbon in bcc iron is calculated. The results show very different conclusions between the nonlocal solutions and the classical ones. The value of the elastic interaction energy obtained by nonlocal elasticity has a good agreement with that measured by a method of internal friction. The classical value, however, is greater than the experimental value.