We propose a direct approach to obtain the boundary stabilization of the isotropic linear elastodynamic system by a "natural" feedback; this method uses local coordinates in the expression of boundary integrals as a main tool. It leads to an explicit decay rate of the energy function and requires weak geometrical conditions: for example, the spacial domain can be the difference of two star-shaped sets.2000 Mathematics Subject Classification: 93D15, 74B05, 93B03, 93B05