The effect of uncertainties in material and geometric parameters on the acoustic performance of a viscoelastic coating is investigated. The model of the coating comprises a structure conventionally used in underwater applications, namely a soft elastic matrix embedded with periodic arrangements of voids. To investigate the effect of uncertainties on the acoustic performance of the coating, stochastic models based on the non-intrusive polynomial chaos expansion (PCE) method and Monte Carlo (MC) simulations are developed. The same analytical formulation of the acoustic coating is employed in both stochastic models. In the PCE method, the analytical model is transformed into a computationally efficient surrogate model using stochastic collocation. The effect of uncertainty in an individual geometric or material parameter on the acoustic performance of the coating is investigated by examining the mean, envelopes, and probability distribution of the monopole resonance frequency and sound transmission through the coating. The effect of variation in combinations of geometric and material parameters is then examined. Uncertainty in the geometric parameters is observed to have greater impact on the resonance frequency of the voids and sound transmission through the coating compared to uncertainty in the material properties.