Summary A reduced order model designed by means of a variational multiscale stabilized formulation has been applied successfully to fluid‐structure interaction problems in a strongly coupled partitioned solution scheme. Details of the formulation and the implementation both for the interaction problem and for the reduced models, for both the off‐line and on‐line phases, are shown. Results are obtained for cases in which both domains are reduced at the same time. Numerical results are presented for a semistationary and a fully transient case.