In Hiroshima Bay, paralytic shellfish poisoning (PSP) caused by the toxic dinoflagellate Alexandrium tamarense has become an annual spring event since 1992. The occurrence of PSP is a serious problem in Hiroshima Bay because the production of cultured oysters from the bay is the highest in Japan. In the present study, on the basis of a physical model which gives advection-diffusion field, the population dynamics of A.tamarense in the estuarine region of Hiroshima Bay was analyzed using a numerical model which simulates species competition with the non-toxic diatom Skeletonema costatum for silicate and phosphate. The Michaelis-Menten equation and the Droop equation were used for nutrient uptake and growth. Grazing by both oysters and zooplankton were also considered in the model. The model reproduced the population dynamics of both A. tamarense and S. costatum as well as silicate and phosphate concentrations in the seawater. Population size of the bloom seemed to be determined mainly by the balance between the water exchange and the growth rate of swimming cells, not by the germination rate of cysts. On the other hand, the termination of the bloom was found to be strongly affected by the encystment process of A. tamarense. Being different from our expectation, grazing processes including the selective feeding by both oysters abnd zooplankton showed no significant effect on the population dynamics of A. tamarense.