An asymptotic analysis for singular stress fields around an interface-edge of dissimilar power-law hardening materials joint has been presented under plane strain condition and J2 deformation plasticity theory. Both the balance of force and the continuity of displacement are satisfied on the interface. In the higher order approximation, the nonlinear effective stress term was expanded by Taylor series. An iteration method is proposed for the determination of singular fields around interface edge. Multiple stress singular terms exist for in the higher order approximation. The order of stress singularity has a dependency with the combination of hardening exponents, .