The stability of extended dislocation barriers in face‐centered cubic metals is determined using the theory of anisotropic elasticity. It is found that the results typically differ from the isotropic elasticity solution by 25%, but the difference can in special cases amount to as much as a factor of four. The anisotropic results are in qualitative agreement with earlier isotropic results in predicting the relative strength of the barriers to dislocation glide. The results suggest that the measurement of barrier extension should provide the most accurate available means of estimating the stacking‐fault energy in fcc metals.