Topology optimization has been extensively considered to design the structural configuration for the stiffness maximization and the eigenfrequency maximization. In this paper, we construct a topology optimization method implementing flexibility with the time-periodic loading condition. First, the flexibility in the dynamic periodic loading is formulated using the mutual energy concept. Second, the multi-optimization problem is formulated using a new multi-objective function in order to obtain an optimal solution incorporating both flexibility and stiffness. Next, the topology optimization procedure is developed using the homogenization design method. Finally, some examples are provided to confirm the optimal design method presented here.