Abstract: In this paper, the radial integration boundary element method is presented to analyze dynamic fracture mechanics problems of functionally gradient materials. The fundamental solutions for homogeneous, isotropic and linear elastic solids are used to derive the boundary-domain integration equations by weighted residual method and this approach leads to domain integrals appearing in the resulting integral equations. The radial integral method (RIM) is employed to transform the domain integrals into boundary integrals and thus the boundary-only integral equations formulation can be achieved. The Houbolt method is utilized to solve the resulted system of time-dependent algebraic equations from the discretization. Numerical results are given to demonstrate the efficiency and the accuracy of the present method.