Abstract: Beams in practical engineering are usually supported by flexible supports, rather than rigid supports, The mechanical model of beams with flexible supports is established in this paper firstly, considering elastic and damping supports and lumped masses at the ends. Based on dynamic differential equations and using finite difference method, the elastic-plastic dynamic responses of beams subjected to dynamic loads are analyzed. The analyzing results show that flexible supports have significant effects on the displacements and internal forces of beams under dynamic loads. Vertical elastic supports tend to reduce the vibration frequencies and the crest values of internal forces and displacements, as a result, the resistances of beams are enhanced by flexible supports. But this advantage depends upon the duration of loads and damping.