The problem of the penny-shaped crack imbedded into an infinite body of an incompressible power-law isotropic material subjected to remote shear stress is addressed in two ways. First, we conduct a detailed numerical analysis using the finite element program ABAQUS. This analysis provides accurate estimates of the discontinuity in the sliding displacements across the crack, and the crack front distribution of the J- integral . A perturbation analysis, proposed earlier in the literature for the corresponding axisymmetric problem, is chosen as an attempt to obtain explicit formulae for the numerical results. Unfortunately, a comparison of the two approaches is not encouraging.