Based on the finite element method, the vibro-acoustic coupling and sound-radiation characteristics of a rib-stiffened cylindrical shell in polar ice-covered waters under very low frequency (VLF) conditions were investigated. A coupled acoustic-structure-fluid numerical model of the sea ice-seawater-rib-stiffened cylindrical shell system was established to analyze the modal characteristics and frequency-domain vibro-acoustic responses under different environmental conditions, as well as the effects of sea-ice thickness and submergence depth on structural vibration, sound radiation, and sound-field distribution. The results show that the external coupled medium affects the natural frequencies of the structure. The effects of sea-ice thickness and submergence depth on the shell-surface vibration are relatively limited, whereas their effects on the sound-radiation response are frequency-dependent. Within the analyzed frequency range of 5-40 Hz, the role of the sea-ice boundary in acoustic-wave behavior changes with increasing frequency. Variations in submergence depth further affect the peak-valley structure of the ice-water interfacial sound field and the distribution of radiation directivity. The results can provide a reference for noise evaluation, submergence depth selection, and acoustic stealth optimization of underwater rib-stiffened shell structures in polar ice-covered waters.