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In this paper, the dynamic response of beams made of bi-directional functionally graded materials (FGMs) with varied cross-sections subjected to a moving harmonic load has been studied by a developed boundary-domain integral equation method based on the two-dimensional linear elastic theory. It is assumed that the elastic modulus and mass density of the FG beams vary separately following each exponential distribution parameters through longitudinal or transvers direction. Then, the elastostatic homogeneous fundamental solution was substituted into the dynamic governing equation for deriving the vibration boundary-domain integral equation of the tapered FG beams. A meshfree scheme can be achieved by applying the radial integration technique to transform the domain integrals into boundary integrals. Houbolt's algorithm is employed to obtain the dynamic response of the tapered FG beams. The …