This paper reviews the applications of singular integral equation (SIE) to the scattering problems of elastic waves by cracks, especially by interface cracks, which were made during past two decades. Several problems such as the reduction of the scattering problems to the SIE, the solution of the SIE and the relationship between the SIE method and other integral equation methods are discussed.Finally, possible applications of the SIE to the scattering problems of cracks are suggested.