The paper considers dynamic characteristics of a vibration protection device with bilinear deformation diagram and hysteresis behavior as part of a system with one degree of freedom. Based on results of the numerical simulation of the system’s response to harmonic effects, the amplitude-frequency characteristics (AFC) of relative displacements and absolute accelerations were constructed. AFC dependences on the limiting elastic displacement and the ratio of the diagram sections stiffness were studied. Based on the AFC, best parameters of a bilinear vibration isolator were determined to reduce the system dynamic response; besides, the nonlinear system resonant frequencies and the damping frequency regions were found.