Identifying the critical location in a stream environment system plays an important role in regulating and monitoring water quality. The critical location is defined as the point of maximum dissolved oxygen deficit within any reach of stream. It is at this location that the threat to the health of the aquatic biota is most severe. Unfortunately, due to the existence of random processes and parameter uncertainties within actual stream conditions, the critical location cannot always be determined with certainty. In recognizing the importance of identifying such a position, this paper attempts to assess the appropriateness of using some of the more common probability distributions to describe the random characteristics of the critical location in a stochastic stream environment. The results from such an assessment could enable one to estimate useful properties of the random critical location such as confidence interval information and the mode of its location. It is believed that this information would have important implications in managing and monitoring stream water quality.