The residence time of slurry is a necessary condition to ensure the mass fraction of underflow in deep cone thickener.In order to explore the relationship between mass fraction of underflow and residence time,the mathematical model between mass fraction and residence time of underflow in deep cone thickener is deduced in this paper.The residence time of the required underflow mass fraction of the deep cone thickener can be obtained by substituting the shape structure and tailings physical characteristic parameters of the deep cone thickener into the mathematical model.An engineering application example of the mathematical model is carried out by using a deep cone thickener in a certain mine.When the mass fraction of the underflow is 55.82 %-70.73 %,the required residence time is 11.75-14.44 h,and the two basically show a linear relationship.If the mass fraction of underflow is more than 68 %,it is recommended that the residence time of tailings in the deep cone thickener be not less than 13.90 h.