Free vibration of two-dimensional functionally graded plates with an exponential material gradation is analyzed in this paper by a meshfree boundary-domain integral equation method. Based on two-dimensional elasticity theory, boundary-domain integral equations are derived by using elastostatic fundamental solutions. Due to the material inhomogeneity and the inertial effect, two domain integrals emerge in the boundary-domain integral equation formulation. Radial integration method is employed to convert the domain integrals into boundary integrals. A meshfree scheme is achieved through approximating the normalized displacements in the domain integrals by a combination of the radial basis functions and polynomials. Thus, the free vibration problem is reduced to a generalized eigenvalue problem, which involves system matrices with boundary integrals only. By using the present meshfree boundary-domain integral equation method, free vibration of twodimensional exponentially graded plates with various material gradients, boundary conditions and aspect ratios are investigated, which demonstrates the high convergence, efficiency and accuracy of the present method.