The quench development process was studied with two six-strand superconducting cable samples with insulated strands and different cabling design. One sample was the traditional ‘six-around-one’ cable, the other was of the ‘round-braid’ type. Quench was initiated by a heating pulse applied to a single strand. A significant difference was observed in the current redistribution among strands due to the different cabling designs. It has an important influence on the stability of multistrand cables. A new concept of the ‘single-strand stability’ was proposed and corresponding stability criteria were offered. A possible way to improve cable stability by using special cabling design is discussed.