This paper shows a methodology that allows the investigation of the effects of random uncertainties on the global dynamics of multistage bladed discs systems. Here uncertainties are accounted for as variations in the material properties of the blades. The multistage cyclic symmetry assumption is used to reduce the deterministic global problem. The random dynamics of the global system is obtained by applying the Polynomial Chaos Expansion. The methodology is applied to a two stage bladed disc assembly and the results of modal and forced response analysis are validated by comparisons with the Monte-Carlo simulations. Possible interactions of multistage mode families in zones of high modal density due to uncertainties in the blades are discussed. Results obtained show that uncertainties may induce significant changes in the global dynamics of multistage assemblies and the proposed technique wants to be efficient to capture those changes. The study classically evaluates the variations of frequencies and responses but also shows that the nature of mode shapes may be drastically affected by uncertainties.