In thin-walled cylindrical pressure vessels (where wall thickness t < r/10), internal gauge fluid pressure generates a biaxial membrane stress state. Equilibrium across longitudinal cross-sections produces circumferential hoop stress (σ_θ = pr/t), while equilibrium across hemispherical end closures produces longitudinal axial stress (σ_z = pr/2t). Because hoop stress is twice longitudinal stress, catastrophic burst ruptures occur longitudinally.