In this paper, uncertainty analysis is carried out on both a simple parametric roll model which can be modeled as a Mathieu equation and a 1.5 degree-of-freedom parametric roll model in regular seas. For both cases, the uncertainty is brought into the system due to the error in predicting the damping coefficients. The non-intrusive polynomial chaos method has been used to assess how the parameters’ uncertainty affects the prediction of parametric roll. The principle aim of this work is to demonstrate computational efficiency without loss of accuracy in probing the effects of parametric uncertainty on ship dynamical systems modeled when using polynomial chaos as compared to the more traditional Monte Carlo method.