A dynamic analysis may be required either because a crack is excited by time dependent loads or because a crack under static loading conditions propagates so rapidly that the effects of the inertia forces are important and the inertia effects cannot be neglected. In this paper, free vibration of the functionally graded beams with open edged cracks are analyzed by a meshfree boundary-domain integral equation method. Elastostatic fundamental solutions are used as weight functions to generate the weighted residual statements of the equations of motion. Fundamental solutions are obtained by considering the inhomogeneous and inertia effects. Numerical results compared well with that of the analytical methods. Comprehensive parametric study investigates the effects of the material gradients and directions, crack length and depth ratios, as well as boundary conditions on the free vibration responses on the cracked FG beams, which demonstrate the present method states high efficiency and accuracy. Besides, the developed method can be used to identify the crack size and location of the FG beams.