In this paper, an element overlay technique (s-FEM [Comput. Struct. 43 (1992) 539]) is applied to various two dimensional linear fracture problems. When s-FEM is adopted, local finite element model concerning cracks can be built independently from the global finite element mesh for modeling overall structure. The local model is superposed on the global one. Therefore, it is tractable to introduce cracks in an existing finite element model. The accuracy of s-FEM is critically examined and it is found that the size of local mesh region needs to be larger than or roughly equal to that of an element in the global mesh.