A dynamic model of a flexible slewing beam in contact with the external environment is developed in this paper. The model is represented in the non-dimensional form. A definition of the percussion center of the flexible beam is introduced and its basic properties are established. It is shown that, contrary to the percussion center of rigid beam, for the flexible beam there exists infinite number of percussion centers, one for the first vibration mode, two for the second, three for the third and so on. It is also shown that the percussion centers can be considered as the points of maximal stiffness of the correspondent vibration modes. The results of our theoretical study may be interested not only for designing flexible tools but also for planning motion strategies for flexible manipulators interacting with the external environment.