The asymptotic analysis of near tip field of plane stress mode II cracks growing quasi-statically in steadiness in power law hardening solids has been performed. Attention was focused on the behavior of the asymptotic solutions as hardening exponent n→∞. Analytical expressions of the dominant terms of velocities and flow factor in centered fan sectors were obtained by expanding them in series of the small parameter s=2/(n-1). Results show that, as n→∞, all the expressions of dominant terms of quantities in near tip field tend to their corresponding ones for elastic-perfectly plastic materials. The effect of hardening exponent n on the angular variations of stresses in near tip field is very weak. Analysis and discussion that related to plane stress mode I crack problem is given in appendix for comparison with results for mode II.