A general methodology is constructed for the fundamental solution of a crack in the homogeneous half-plane interacting with a crack at the interface between the homogeneous elastic half-plane and the nonhomogeneous elastic coating in which the shear modulus varies exponentially with one coordinate. The problem is solved under plane strain or generalized plane stress condition using the Fourier integral transform method. The stress field in the homogeneous half plane is evaluated by the superposition of two states of stresses, one is associated with a local coordinate system in the infinite fractured plate, while the other in the infinite half plane defined in a structural coordinate system.