AbstractA new semi analytic method for solving two dimensional elastodynamic problems in semi-infinite medium is proposed. The elastodynamic field equations are Fourier transformed in the infinite space dimension(s), while time derivatives are approximated via finite difference, leading to a set of ordinary differential equations in the semi infinite direction(s), which are solved analytically. The method is inherently non-reflecting and no artificial boundaries are used. 1 and 2-D examples of a rigid body impact are studied and the non-oscillating characteristic of the solution, usually obtained by other methods, is examined. The accuracy is examined by comparing the results with solutions obtained by previous methods.