The object of the present study is to investigate the influence of damping uncertainty on the frequency response of a dynamic system with many degrees of freedom. A statistical linear model is presented which allows a probabilistic description of the response in terms of second-order statistics. The limits of validity of the linearization technique are investigated by means of a Monte Carlo simulation. An original hypothesis regarding the statistical correlation of damping coefficients is formulated. The theory as developed is applicable to different forms of damping and to other system parameters. A numerical example based on a five-degree-of-freedom system shows quantitatively the importance of an accurate estimate of the damping coefficients for lightly damped systems in the neighborhood of a natural frequency.