It is generally believed that stress wave superposition does occur and plays an important role in cutting blasting with a single free surface, in which explosive columns of several blast holes with short spacing are simultaneously initiated. However, considering the large scatter of pyrotechnic delay detonators that are used in most underground metal mines in China, the existence of stress wave superposition and the influence of this effect on rock fragmentation are questionable. In the present study, the stress wave interaction in short-delay blasting with a single free surface was studied through the use of the LS-DYNA code. Stress waves induced by two blast holes blasting with different delays were compared with the single blast hole case, and the effects of delay time, detonating location and spacing on stress wave superposition were investigated. The numerical results showed that for blast holes with a 1 m spacing, stress wave interaction only occurs when the delay time is 0 ms and does not occur for blasting with delays of more than 1 ms. An increase in the duration of a stress wave via optimizing the detonation location does not improve the stress wave interaction. For a 1 ms delay, stress wave superposition only occurs when the spacing is more than 4 m, which is a rare case in practice. The results indicated that the occurrence of stress wave superposition for blasting with a single free surface is strictly limited to conditions that would be difficult to achieve under the existing delay accuracy of detonators. Therefore, it is unrealistic to improve fragmentation via the stress wave interaction in field blasting. Furthermore, the numerical results of the stress wave interaction also show that there would be a great potential to reduce the hazardous vibrations induced by short-delay blasting by using electronic detonators with better control of delays in an order of several milliseconds.