In this paper, a method for optimal placement of sensors and actuators is presented by using new measures of modal controllability and observability defined in a balanced coordinate system. The proposed new measures are shown to have a great advantage in practical use when they are used as criteria for selecting the locations of sensors and actuators, since the most controllable and observable locations can be obtained to be identical. In addition, they are more accurate than the measures of Hamdan and Nayfeh in that the effects of the eigenvector norm are considered into the magnitude of measures. In simulations, to verify the effectiveness of the proposed measures and optimal placement method, the closed-loop response of a simply supported flexible beam, in which the number and locations of actuators are determined by using the proposed measures and optimal placement method, has been examined and compared with the case of Hamdan and Nayfeh’s measures.