With high international oil price, the exhaustion of onshore resources and declination of oil and gas production in shallow sea, deep water has become the important succeeding area of worldwide oil and gas. During deepwater oil and gas development, riser must be used to isolate seawater, circulate drilling fluid, and compensate the heaving movements of the string and so on. However, with the operating water depth increasing, the loads of waves and ocean currents on the riser become more complex, leading to extremely high construction risk and funds risk of deep-water operations. In this paper, considering the combined action of inside and outside fluid on the riser, transverse vibration partial differential equation is derived, and solved with finite difference method. Meanwhile, transverse displacement response of the riser acted by outer load is determined, and the shear force, bending moment and bend angle at different locations are solved, then the influence factors of riser transverse vibration are analyzed. The mechanical analysis of marine riser can provide a theoretical guidance for safe and effective drilling work, which is of great significance for the offshore oil and gas development.