Abstract: Based on elastodynamics, employing the complex function and conformal mapping method, elastic wave scattering and dynamic stress concentrations in exponentially graded materials with a cavity of arbitrary shape have been investigated and an analytical solution of the problem has been derived.The numerical results of the dynamic stress concentration factors around the elliptical cavity are presented as an example. The effects of elastic wave-number and heterogeneous parameters of the materials on the dynamic stress concentration factors are analyzed.