An analytical-numerical method is developed for studying the diffraction of elastic wave by an abnormal cylinder embeded in layered media. The method is based on a combination of partial separation of variables and fractional steps difference techniques in cylin-drical coordinate system. For examining the efficiency of this method a calculation example is given.

Some methods of fractional steps for solving initial-boundary problems of two dimensional elastic wave equations which describe the P-SV wave propagation generated by linear compressional source in the 2-D hemi-indefinite space with discontinuous coefficients are discussed. A boundary condition is provided by the contribution of source. For examining the efficiency of these methods, two calculation examples are given.