The present research concerns the uncertainty propagation of a fluid-structure dynamical system, taking into account the geometrical nonlinearities of the structure induced by the large deformations and the large displacements. The structure is coupled with an internal cavity filled with a linear acoustic liquid. A nonlinear-reduced order model adapted to such internal vibroacoustic problem is first numerically constructed in order to reduce the size of the problem. The formulation is carried out with displacements and pressure unknowns for the structural and acoustic part respectively. The uncertainties are then implemented with the nonparametric probabilistic approach. In particular a dedicated stiffness operator self-containing the information relative to the geometric nonlinearities is constructed. Note that a peculiar attention that allows the uncertainties on the nonlinear part to be coherently taken into account is made. The methodology is presented through a numerical application consisting in a finite element model of a coupled fluid-structure system. [1] R. Ohayon and C. Soize, Advanced Computational Vibroacoustics - Reduced-Order Models and Uncertainty Quantification, Cambridge University Press, Cambridge, 2014. [2] E. Capiez-Lernout, C. Soize, M. Mignolet. Computational stochastic statics of an uncertain curved structure with geometrical nonlinearity in three-dimensional elasticity. Computational Mechanics, Springer Verlag (Germany) 2012, 49 (1), 87-97.