A multiple-fold umbrella shaft, consisting of a plurality of tubes telescopically engageable with one another, includes an inner tube having concave quadrants designated as Vi, and an outer tube slidably engageable with the inner tube and having concave quadrants designated as Vo, forming a relationship as defined by a formula of Vi-Vo.gtoreq.1 in order for preventing twisting and vibration of the tubes and for enhancing a smooth folding or unfolding operation when closing or opening the umbrella.