Understanding of modal characteristics of fluid–structure interaction (FSI) systems plays a vital role in avoiding large oscillations and instabilities. Further, with parametric uncertainties, the onset of the instabilities may change and hence it is important to know the statistics of the modal characteristics of the coupled system to avoid system failures. The primary objective of the study is to estimate the statistics of modal characteristics of the stochastic FSI system which demands intensive computation resources especially for large ordered FSI systems. The present study also focusses on developing and implementing a stochastic reduced-order model to resolve pressure-induced oscillations of a disc-like structure as a generic fluid–structure interaction system. The stochastic reduced-order model uses a modal reduction approach together with spectral projection-based polynomial chaos expansion (PCE) to truncate both the system degrees of freedom (dofs) and the random modes. Interfacing algorithms have also been developed that enable finite element (FE) modelling of the FSI system using commercial software and in-house developed codes. © 2019, Springer Nature Singapore Pte Ltd.