A method is given for calculating vibration isolation systems with a viscous dampers as nonlinear systems with single and two degrees of freedom. Nonlinearity is determined by the inclusion  of additional dissipative forces in zones of large displacements (near resonant zones at start-up and shutdown of equipment). The method is illustrated by an example of calculating a system with single degree of freedom. The results of the calculation shows that the inclusion of viscous friction dampers in the transient modes makes it possible to significantly reduce the levels of oscillations during passage through the resonance, and the maximum displacements in the resonance zone are  practically independent of the time intervals in the starting and  stopping modes.