During the operation of vanadium redox flow battery, the cell stack can suffer from electrolyte leakage and material failure that significantly affect the overall performance of the battery, provided that the stack is improperly designed and assembled. In order to manufacture more reliable battery stacks without undergoing electrolyte leakage and mechanical failure, the stress distributions on all key components of the stack need to be known. In this study, three-dimensional mechanical models are developed to perform simulation analyses on stress distribution for the cell stacks. Stress distributions on key cell components under specified sealing gasket designs, assembling forces and number of cells in a stack are investigated for the single cell and multi-cell stacks, while potential material failure and damage for the stack components are also analyzed in accordance with maximum stress criterion and von Mises yield criterion depending on the material of the components. Simulations results successfully demonstrate the stress distribution and magnitude in specified stack design and assembly condition, and highlight the importance of mechanical analyses in developing flow battery stacks with superior sealing and mechanical performance for long-term use.