A pressure test on a liquid-helium vessel with the niobium cavity in a cryostat to the maximum allowable operational pressure is required as the main item for a safety test near 300 K, to prepare for application for a license to operate a superconducting radio-frequency (SRF) module. Because the niobium cavity has a shell structure and is part of the liquid-helium vessel, to prevent its buckling during test at high pressure becomes a critical issue in designing a 500-MHz SRF module. To meet the safety requirement, currently available 500-MHz SRF modules hence have a limit on the maximum allowable operational pressure that is marginally above the routine operational pressure. Safety devices such as relief valves are, correspondingly, chosen to meet the pressure limit at only 10 or 20 kPa above the operational pressure, thus causing operational inconvenience and a risk of damage of the shell-like cavity structure. A local reinforcement of the cavity is proposed herein to increase its buckling strength and thus its maximum allowable operational pressure. Illustrated with a 500-MHz SRF cavity of KEK type, detailed investigations of its elastic buckling modes and the corresponding strengths are computed with linear, 3-D, and finite-element models to determine an optimized geometry and the location of the reinforcement rings. Variations of the corresponding buckling modes and stress distributions are examined. Although the required tuning force is slightly increased but within an acceptable range from an engineering point of view, maximum allowable operational pressure of the 500-MHz SRF module can be effectively increased up to 200 kPa or even more when properly implementing one pair of reinforcement rings on the niobium cavity cell.