Abstract: A mathematical model of turbidity currents flowing down from continental shelves to continental slopes is presented in this study. The layer-averaged momentum and continuity equations of turbidity currents, and the dispersion equation of suspended sediment are integrated with the use of a regularity condition satisfied at the Richardson critical point between continental shelves and continental slopes. The results of the analysis show that steady turbidity currents flowing from continental shelves to continental slopes can be realized only when the critical layer thickness is smaller than a certain value. It is also found that turbidity currents are mildly accelerated on continental slopes while turbidity currents are decelerated on continental shelves in the downstream direction. These results suggest that only turbidity currents with sufficiently large suspended concentration can reach the Richardson critical point, and that turbidity currents flowing from continental shelves to continental slopes have to be generated somewhere not far upstream from the Richardson critical point.