Abstract: It is difficult to calculate normal water depth of a arched section tunnel for its complex geometrical shape. From using the mathematics transformation method and the theory of optimization and regression to deal with the basis equation of the normal depth in arched section tunnel，a new direct formula is derived in this paper，which overcomes the shortage of other methods，such as chart looking up method，trial and error method and iterative trial method．This method is simpler and more accurate than other approximate methods with a maximum error of less than 0.40% in the utility range (ratio of critical depth to arch radius of 1.0-1.80). So, it will be useful in engineering practice and in course of compiling handbook of hydraulic structure design.