The selection of the number, type and placement of sensors to monitor a vibrating system is critical to obtain accurate predictions of the health of the system and to define closed-loop control systems. This paper proposes a novel methodology that solves the sensor placement problem using machine learning algorithms. The sensor placement problem is formulated as a feature importance selection process, in which the features which have most impact on the output are selected by the machine learning models. The features correspond to the instantaneous signals measured by each possible sensors; the output corresponds to the metric of interest. In this paper, the Random Forest feature selection approach is applied to the sensors’ selection of a vibrating beam. Several locations for strain gages and accelerometers are considered as features of the machine learning model. Three different outputs are considered, specifically maximum axial stress, maximum axial strain and maximum acceleration.