The computational method of S(t)curve in instantaneous unit hydrograph is a difficult point inthe research on computation ofengineering hydrology.At present,the method still has some shortcomings in prac-tice,so we have transformed its mathematical expression,made it to be evaluation of gamma distribution function,and given its general analytic expression and estimation formula on truncation error.Proved by practice,itsmathematical model is simple,flexible,and has the advantage of high precision,saving of memoryspace. stronggenerality,high convergence speed,good numerical stability and etc