In this paper, the problem of mathematical modeling of nonlinear longitudinal vibrations of a hysteresis-type elastic dissipative characteristic beam with a liquid section dynamic absorber under the inuence of kinematic excitations has been considered. In this case, the method of bond graph was used in mathematical modeling. As a result, the system of dierential equations of motion was expressed by rst-order derivatives of momentum and velocities. Mathematical models of several special cases were derived from the system of dierential equations of motion, and the reliability of the obtained results was shown.