Under the condition that all the stress components at a crack-tip are the functions of θ only,making use of the equations of steady-slate motion,stress-strain relations and Hill anisotropic yield conditions,we obtain the general solutions at a crack-tip in both the cases of anti-plane and in-plane strains.Applying these general solutions to the concrete cracks,the anisotropic plastic fields at the rapidly propagating tips of mode Ⅲ and mode Ⅰ cracks are derived.