Abstract: Three-dimensional governing differential equations are derived based on the linear elasticity theory and the equations are discretized using the meshless collocation method based on the inverse multiquadrics radial basis function. Through the numerical examples, the convergence characteristics and the choice of shape parameter are studied. It is found that the natural frequencies computed with shape parameter . (N_xis the number of node at the xside) converge most rapidly. The natural frequencies of orthotropic and isotropic plates under different boundary conditions are calculated by the proposed method. The proposed results are in good agreement with the available published results.