The objective of present study is to present solution to determine the stress and displacement fields around an interface edge of a joint formed by quarter planes in which materials behaves as an elastic and a power-law hardening material. J₂-deformation plasticity theory under plane strain condition is assumed for the power-law hardening material. Both the balance of force and the continuity of displacements are satisfied on the interface iteratively. The stress fields are found to be singular with the type of r^{λ_i -1} singularity from the i-th order approximation, where r is the radial distance from the interface. The power of r in the stress equation depends on the hardening exponent n. (i +1) or more singular terms exist in the i-th order approximation for n < (i +1)/i .As n is increased the absolute value of the i-th order of singularity, |λ_i-1| ,tends to be decreased to zero when λ_i-1<0.