Abstract A damping mechanism is universally seen in vibrating systems, such as flexible structures and robotic manipulators. However, its nature is still little understood and the modelling technique so far has been primitive. This work, by introducing the Method of Energy Approximation (MEA), provides a unified approach to nonlinear damping modeling and random response analysis of single-d.f. vibrating systems. By the MEA, one can easily find the approximate but closed-form stationary probability density function (i.e. the stationary solution of the Fokker-Planck equation) of any nonlinearly damped vibration subject to white noise excitation. Various results validating the MEA are obtained. The central result of this work is the establishment of an efficient method for the modeling of a nonlinear damping mechanism based upon free response data. It is also found that, among all choices of nonlinear damping models, energy type nonlinear damping models of the form μ ( ω 2 0x 2 + x ̇ 2 2 ) x ̇ (t) play a central role and their relation to all other nonlinear damping models is thoroughly studied.