Rear-end crashes on congested freeways are among the most frequently occurring capacity-reducing incidents. Empirical evidence suggests that freeway rear-end crashes tend to occur when stopping shock waves form on freeways. To understand the occurrence of such incidents, this study determined conditions by which a stopping wave results in a rear-end crash. Reviewing the existing literature on rear-end crash mechanisms, the study first established a sufficient condition for a shock wave to produce a rear-end crash and then verified it by using video recordings of 41 shock waves, including five resulting in rear-end crashes, on Interstate I-94 in Minneapolis, Minnesota. For each shock wave, key kinematic features of the involved drivers, including initial speeds, following headway, average decelerations, and reaction times, were estimated. The proposed crash condition successfully distinguished between successful brake-to-stop events and rear-end crashes. Detailed analysis of two rear-end crashes illustrated how drivers with reaction times longer than their following headways played a key role in determining the crash outcome of a shock wave. These findings suggest that interventions focusing on the relationship between reaction time and following headway could reduce the frequency of rear-end crashes.