The main objective of this study is to examine the two dimensional surface crack problems in a system with an interface between two elastic-plastic solids of different yield strength subjected to mode I mechanical loading. The surface cracks growth is considered to occure along the interface direction of bimaterials which is perfectly bonded to each others. A two dimensional finite elementmethod is used to solve the structural problem. Solid 183-node elements are utilized to simulate the strain singularity around the crack front. The crack surface is subjected to a compressive load by three point bending. The stress intesity factors are computed by using the displacement correlation technique. The primary goal is to develop a model crack tip stresses and strains in a manner that is useful for crack growth initiation and propagation in a FGM.