Research by Gast and Bournia on nuclear reactor cores in the form of elliptical cylinders is revisited. Derivations are presented, and data are extended in scope and accuracy. Findings on asymptotic series for constants needed in the evaluation of Mathieu functions are reported, along with accurate alternative techniques. Geometric bucklings are expressed in terms of circular cylinders with equivalent surface-to-volume ratios in a form that allows easy interpolation from tables. The estimation of extrapolation distances at boundaries of elliptical systems is addressed. Applications considered include a possible research reactor, the damage of fuel storage/shipping casks, and decommissioning of the damaged Windscale reactor.