In this paper nonstationary vibrations are studied by means singular spectrum analysis (SSA) – a model-free method of time series analysis and forecasting. SSA allows decomposing the nonstationary time series into trend, periodic components and noise and forecasting subsequent behavior of system. The method can be successfully used for processing the signals from the vibrating constructional elements and machine parts. This paper shows application of this method for random and nonlinear vibrations study on the examples of construction elements vibration under seismic action.