Liquefied gases, such as chlorine or ammonia, are stored in large quantities on industrial sites. If released accidentally, they can form a heavy gas cloud that has the potential to kill or injure large numbers of people. The dispersion of such a cloud is thus of interest to the risk assessment community. This is the first of a two-part paper. Here, the risk (probability) of being exposed to a continuously released toxic gas cloud, given a release, is considered; probability language is needed because wind direction is assumed to be a random variable. Part II considers instantaneous releases. Risk is considered in terms of RC; the probability at any point of receiving a non-zero dose given a continuous release. For flat ground, simple analy...