In its 90 years of life, the Tuned Mass Damper have found application in many fields of engineering as a vibration reducing device. The evolution of the theory of TMDs is briefly outlined in the paper. A generalised mathematical linear model for the analysis of the response of line-like structures with TMDs is presented. The system matrices of the system including the TMDs are written in the state space as a function of the mean wind speed. The stability of the system can be analysed and the Power Spectral Density Function of any response parameter calculated, taking into account an arbitrary number of modes of vibration as well as an arbitrary number of TMDs, for any given PSDF of the excitation. The procedure can be used to optimise the number, position and mechanical properties of the damping devices, with respect to any response parameter. Due to the stationarity of the excitation, the method is well suited to structures subjected to the wind action. In particular the procedure allows the calculation of the onset galloping wind speed and the response to buffeting, and a linearisation of the aeroelastic behaviour allows its use also for the evaluation of the response to vortex shedding. Finally three examples illustrate the suggested procedure.