Rotating machines are major components in mechanical engineering, for instance in aeronautics and energy production with nuclear and hydroelectric power plants. These structures are subjected to high loading and vibration stresses, which tend to reduce their operating life. Yet, their paramount role urges engineers to develop tools to understand their dynamic behaviour in order to ensure their integrity. The severe strains occuring when the rotor passes through its critical speeds jeopardize the structure. Thus, accurate knowledge of the two quantities of interest (QoI) — critical speeds and maximum strain amplitudes — is crucial in order to avoid premature damage. However, design parameters, at the core of the vibration properties, are under numerous sources of uncertainties due to measurement or manufacturing operations, implying a disruption of these properties. It is therefore necessary to quantify the impact of such uncertainties on the QoI to ensure a reliable design. Nevertheless, performing numerically expensive calculations in such a high dimensional uncertainty domain is unaffordable with a usual method, namely the Finite Element Model. In this context, surrogate models prove to be appropriate substitution methods, only requiring a few costly queries for training. Since any further use of the surrogate is costless and accurate, vibration properties of any uncertain rotor can be easily determined. More generally, uncertainty propagation and quantification can be efficiently performed. Gaussian processes are used for this purpose. Low computing costs allow massive calculations, enabling a sensitivity analysis to be accurately carried out, based on linear and Sobol indices. This analysis not only allows to rank the uncertain parameters according to their overall importance on the rotor dynamic quantities, but also classifies their influence: linear and non-linear impact alone, and interactions between them. It is highlighted that the QoI undergo various impacts, providing deep insights and understanding in the dynamic of the system.