A stochastic model for stream pollution is given in terms of a random differential equation of the form X(t) = AX(t) + Y(t), 0 ≤ t ≤ Q, where X(t) is a two‐dimensional vector stochastic process giving the biochemical oxygen demand (BOD) and dissolved oxygen (DO) at distance t downstream from a major source of pollution. The random inhomogeneous term Y(t) is a function which may be chosen to allow various patterns of discharge of effluent into the stream. In particular, in this paper Y(t) is assumed to describe a discharge of pollutant along a continuous stretch of stream in addition to a point source of pollution at t = 0. The joint probability distribution of BOD and DO at each t is derived for several cases, and computer simulated trajectories as well as the mean and variance functions are presented which indicate the statistical properties of the BOD and DO processes.