Abstract: Based on the complex function theory, scattering by elastic waves around a homogeneous circular inclusion buried in a radially inhomogeneous elastic medium is investigated in the paper. The inhomogeneity of the medium is assumed that the density depends on the radial distance as a power-law function and the shear modulus is constant. Inhomogeneous wave equation with variable coefficient is converted to the standard Helmholtz equation by using the coordinate transformation. The expressions of displacement and stress fields in complex coordinate are presented due to the existing of both the inhomogeneous base and homogeneous inclusion. The dynamic stress concentration factor (DSCF) around the inclusion is illustrated numerically by examples. Results show that wave number and shear modulus ratios between the base and inclusion, wave number of the base, inhomogeneous parameter have great influence on the dynamic stress concentration.