This paper presents an optimum design method for mechani- cal structures considering harmonic loads using a level set-based topology optimization method and the Finite Element Method (FEM). First, we briefly discuss the level set-based topology op- Timization method. Second, a topology optimization problem is formulated for a dynamic elastic design problem using level set boundary expressions. The objective functional is set to mini- mize the displacement at specific boundaries. Based on this for- mulation, the topological sensitivities of the objective functional are derived. Next, a topology optimization algorithm is proposed that uses the FEM to solve the equilibrium and adjoint equations, and when updating the level set function. Finally, several numer- ical examples are provided to confirm the validity and utility of the proposed method. © 2012 by ASME.