From a mathematical viewpoint, the frequency domain analysis of vessel motion responses due to wave actions is based on integration of system dynamics idealized in terms of response amplitude operators (RAOs) for 6 DOF rigid body motions and an input wave spectrum in order to obtain the response spectrum. Various quantities of interest can be deduced from the response spectrum which are then used for deriving response-based operational limits for marine operations, also including extreme value and fatigue analysis. The variation of such quantities, owing to the uncertainties associated with the vessel system parameters, can be quantified by performing uncertainty propagation (UP) and consequent sensitivity analysis (SA). This study emphasizes and proposes a computational-efficient way of assessing the sensitivity of the system model output with respect to the uncertainties residing in the input parameters by operating on a surrogate model representation. In this respect, the global sensitivity analysis was effectively carried out by deploying an efficient non-intrusive polynomial chaos expansion (PCE) surrogate model built using a point collocation strategy. Successively, the Sobol' indices were obtained from the analytical decomposition of the polynomial coefficients. The indices, eventually, are employed to quantitatively measure the effects of input uncertainties on the output 6 DOF vessel Root Mean Square responses.