Abstract: Riser system is one of the major equipments in offshore drilling.This paper simplifies the four-order nonlinear partial differential equation and the boundary conditions describing the marine riser motion,and numerically simulates the nonlinear dynamic analysis by using a finite-difference method.Then the top tension on the drilling riser is studied in four sea states and the corresponding counting programs are made.The results obtained through the calculation of different pratical examples prove to be identical with those by stress Engineering service Inc.U.S.A.The top tension analysis method and the counting programs in this paper prove to be simple，accurate and time-saving，thus they are of practical use in the design and check of the drilling riser system.

Key words: Offshore drilling platform, Riser, Stress analysis, Mathematical model, Numerical analysis