Shop–welded, flat-bottom tanks for storage of production liquids are designed and fabricated in specific dimensions and capacities for internal pressures close to atmospheric pressure in accordance with the API 12F specification. This study addresses the failure pressure on the eleven (11) current API 12F shop-welded steel tanks as well as two proposed sizes through finite element and stress analysis of more than 350 different tank models. An elastic analysis was carried out to determine the yielding pressure of the shell-to-bottom and roof-to-shell joints. An elastic buckling analysis and a post-buckling analysis including imperfections was performed to determine the buckling modes of the equipment. The redistribution of stresses due to inelastic deformations and plastic collapse were evaluated through a plastic stress analysis considering the stress–strain hardening of the ASTM A36 mild steel material. Moreover, the design pressure increase to failure pressure or 24 oz/in2 (10.3 kPa) was investigated regarding the stress levels and bottom uplift of the 13 flat-bottom tanks. The presented research provides meaningful insights and engineering calculations to evaluate the current design of the API 12F shop-welded, flat-bottom tanks as well as to establish new design internal pressures guaranteeing a safe performance of the equipment.