The object of the present study is to investigate the influence of damping uncertainty and statistical correlation on the dynamic response of structures with random damping parameters in the neighbourhood of a resonant frequency. A Non-Linear Statistical model (NLSM) is successfully demonstrated to predict the probabilistic response of an industrial building structure with correlated random damping. A practical computational technique to generate first and second-order sensitivity derivatives is presented and the validity of the predicted statistical moments is checked by traditional Monte Carlo simulation. Simulation results show the effectiveness of the NLSM to estimate uncertainty propagation in structural dynamics. In addition, it is demonstrated that the uncertainty in damping indeed influences the system response with the effects being more pronounced for lightly damped structures, higher variability and higher statistical correlation of damping parameters.