The bending stresses of top tensioned riser(TTR)under combined excitations of currents, random waves and vessel motions are presented in this paper, and the effect of the internal flowing fluid on the riser stresses is also considered. The computation programs which are used to solve the differential equations in the time domain are compiled and the principal factors of concern including the angular movements at the upper and lower ends of the riser, lateral displacements and bending stresses are presented. Then the effects of current velocity, random wave, top tension, vessel mean offset, low frequency motion and internal flow velocity on the bending stresses of the riser are analyzed in detail.