As a particular instance of the complete acoustic radiation problem for an underwater structure, structure-borne noise radiated from a combined submarine-propeller system under self-propulsion condition is investigated. The analysis procedure applies a set of numerical methods to capture different aspects of the problem: unsteady computational fluid dynamics to express the hydrodynamic excitation, finite element analysis to obtain the dynamic characteristics of the combined elastic system, and boundary element method to assess the radiated noise owing to structural vibrations. The structural and acoustic responses rely on the modal descriptions. The study has three objectives: employing the methodology in a realistic setting, investigating the validity of the proposed approximate configurations, and studying the influence of propeller blade flexibility on noise radiation. The DARPA-SUBOFF submarine and INSEAN E1619 propeller models are adopted for the application. It is found that approximate configurations provide accurate estimations for limited frequency bands and should be employed with caution. In addition, the flexibility of the propeller plays a major role in noise generation, not only by yielding higher noise levels but also by increasing the amplitude of the peak responses in the low- and high-frequency regions.