Stability of multi-strand superconducting cable against local disturbances has been studied experimentally and theoretically. Quench experiments have been made with a superconducting triplex cable made of chrome-plated strands. A heat pulse is applied to a short part of one strand, and the minimum quench energy (MQE) against that local disturbance and the temporal evolution of the strand current during the quench or recovery process are measured. When the transport current divided by the critical current (I t /I c ) is large, the MQE against a local disturbance almost equals the MQE of the single strand. When the overall I t /I c is less than 0.4, the MQE against a local disturbance is much larger than the MQE of the single strand. In this small I t /I c region, when a heat pulse whose energy is slightly less than the MQE is applied, current re-distribution is observed during the recovery process. Numerical simulations of the quench or recovery process have been made with a computer code named MST. The dependence of the calculated MQE on the I t /I c qualitatively agrees with the experimental result. The numerical and experimental results prove that the stability against local disturbances is improved by the current re-distribution when the I t /I c is less than some threshold value. This threshold appears to be influenced by the contact thermal conductance between strands.