Method of elastic stress analysis for general Functionally Gradient Materials (FGMs) with 2D crack is studied based on the principle of superposition In the present study, the spacial variation of the elastic constants is expressed by an embedded force doublets in an elastic continuum. As a result, the stress field of an arbitrarily gradient materials is expressed by the superposition of Kelvin's solution for a homogeneous body. In the present study, a center cracked rectangulate plate whose Young's modulus varies with spacial coordinate was analyzed numerically.