The mechanical properties of superconductors such as Young's modulus and yield strength, are very important for their applications. There has been an urgent need to test the mechanical properties, but no standard method exists worldwide. We have discussed, evaluated through a round-robin test, and standardized the method of room temperature tensile tests for Cu/Nb-Ti composite superconductors because Cu/Nb-Ti composite is now the most popular superconductor. This paper provides critical examination of this method and is concerned with double-yielding phenomena, strain measurement, reliability, and accuracy, which are the items to be elucidated. The first draft is prepared and submitted to IEC/TC90 as an international standard. It will soon be issued as International Standard IEC61788-4.