The energy of a shear dislocation ring is calculated in the framework
of the Peierls model in which the displacement is represented by a den
sity of infinitesimal dislocations in the glide plane. This avoids the
introduction of an uncertain core cut-off radius r(0) to prevent dive
rgence in the usual treatment. The atomic misfit energy in the glide p
lane is accounted for explicitly and the influence of the interplanar
potential on the ring energy and the core structure is studied. Wherea
s spontaneous formation of shear rings in a homogenous stress field ca
n be ruled out, the emission of dislocation rings from crack tips in g
lide planes not containing the crack front is feasible.