In a two-layer superconducting cable, we numerically investigated the effect of magnetic properties and alignment of the substrates of the tapes on the stress distribution induced by a very high transported electric current. The calculations are carried out for two tapes, with one being on top of the other. Sharp peaks of induced stress very close to the edges of the tapes are observed. When nonmagnetic substrates are used, the stress distributions on the tapes are almost identical, as well as being much lower than those in the cases involving ferromagnetic (FM) substrates. When the tapes are arranged face to face with FM substrates on the outer sides, the stress distribution arisen in the outer tape is considerably higher than that in the inner tape. In contrast, flipping both layers, so that the tapes are back to back, gives rise to a much lower stress over the outer tape than that over the inner tape.