A novel approach in analysing the vibration of elastic body systems is presented and discussed in this paper. This method uses a meshless spatial approximation based only on nodes, which constitutes an advantage over the "nite element method. As it is applicable to an elastic body with arbitrary shape, it also has advantages over the classical Rayleigh}Ritz method and its extensions. The paper is organized as follows: in Section 2, Hamilton's principle is used for obtaining the equations of motion for a three-dimensonal simply connected elastic body. In Section 3, the development of weighted base functions for the moving leastsquares interpolant is described. In Section 4, the mass and sti!ness matrices are derived using the previous results. In Section 5, a system synthesis description is given, in which we also develop the approach used for integrating the boundary conditions. Finally in Section 6, the theoretical results are validated by case studies chosen to highlight various features of the approach, including optimization of the shape function parameters. The particle method has already been used for structural dynamics (Liu et al., International Journal for Numerical Methods in Engineering 1995;38:1655}1679), but for free vibration of beams and plates, to the authors knowledge, this paper is the "rst application of the element-free method to modal analysis.