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During severe seismic events the base of unanchored steel liquid-storage tanks can uplift, causing large inelastic rotation demands at the shell-to-base connections and large multi-axial stresses (radial tension and circumferential compression) in the tank base-plate. With repeated cycles of uplift, these shell-to-base connections are susceptible to low-cycle fatigue failure. Limited research exists on the rotation capacity of shell-to-base connections, and the studies that have been conducted have neglected the multi-axial stress states in the tank base-plate. In this paper, an analytical study is conducted to determine the effects of these multi-axial base-plate stresses on the rotation capacity of tank shell-to-base connections. Modeling methods and a low-cycle fatigue failure criterion are validated using experimental results, and then twenty-three models with varying multi-axial stress states are analyzed under various ranges of cyclic rotation. Results indicate that moderate levels of base-plate radial tension and circumferential compression (between 10 and 20%y) can significantly reduce connection rotation capacity (between 28-48%). Additionally, due to increased yielding from circumferential stresses at low rotations, smaller uplift cycles may contribute more to failure than previously reported in studies neglecting base-plate multi-axial stress-states. Indicated rotation capacities are larger than current code limits.