Vibrations are classified among the major problems for engineering structures. Anti-vibration isolators are used to absorb vibration energy and minimise transmitted force which can cause damage. The isolator is modelled as a parallel combination of stiffness and damping elements. The main purpose of the model is to enable designers to predict the dynamic response of systems under different structural excitations and boundary conditions. A nonlinear identification method, discussed in this paper, aims to provide a tool for engineers to extract information about the nonlinear dynamic behaviour using measured data from experiments. The proposed method is demonstrated and validated with numerical simulations. Thus, this technique is applied to determine the nonlinear parameters of a commercial metal mesh isolator. Nonlinear stiffness and nonlinear damping can decrease with the increase in the amplitude of the base excitation. The softening behaviour of the mesh isolator is clearly visible.