A polygonal scaled boundary finite element method (SBFEM) is proposed for linear elastodynamics in two dimensions. The domain is divided into non-overlapping polygonal elements, and the scaled boundary finite element approach is employed over each polygon. The advantages are that an arbitrary interpolation order can be used on each polygon and we can choose the optimal element order on each edge individually. Moreover, the SBFEM simplifies the numerical integration over the polygons when compared to conventional approaches. The dynamic stiffness matrix is computed by employing the continued fraction expansion. The influence of the shape of the polygon and the element order on the boundary of each polygon are studied. The robustness and the accuracy of the approach are demonstrated with numerical examples. © 2018 Elsevier B.V.