For A.C. application, superconducting strands are bundled and twisted to make a cable with large current capacity. The quench characteristic of the cable depends on the contact thermal and electrical conductivities between strands, significantly. For improvement of the stability of non-insulated multi-strand cables, it is necessary to decrease the local rise of temperature by the Joule heating in the current redistribution among strands. For this purpose, we have analytically investigated non-insulated strand cables in which the surface of each strand is covered with Cu-sheath. The transient stability of this cable is discussed analytically and experimentally.