We propose an efficient Monte Carlo simulation method to address the multivariate uncertainties in acoustic–vibration interaction systems. The deep neural network acts as a general surrogate model to enhance the sampling efficiency of Monte Carlo Simulation. Singular Value Decomposition - Radial Basis Functions (SVD-RBF) acts as a bridge between the original full model and the neural network, enabling the training datasets of the neural network to be evaluated rapidly from a reduced-order model. The snapshots of full order models are obtained with isogeometric analysis, in which we couple two numerical schemes for vibro–acoustic interaction problems: the isogeometric finite element method for simulating vibration of Kirchhoff–Love shells and isogeometric boundary element method for exterior acoustic waves. Numerical results show that the proposed algorithm can significantly improve the efficiency of uncertainty analysis.