Construction of an improved mathematical model of the axial and lateral oscillations of the in the plane of action of the velocity vectors of the fluid flow washing the was considered. This model makes it possible to study the stress-strain state of the with simultaneous impact on it from the sea and the change in the force of tensioning its upper end. In addition, the model specifies the force effect exerted on the by the washing fluid flowing in it.Based on the developed mathematical model, a simulation model of operation of the drilling ship – rope-type tensioning system of the – riser system was created in the Modelica modeling language and a series of numerical experiments were performed at various levels of seaways. The obtained results show that the proposed model produces 22‒40% higher calculated values of the amplitude of lateral oscillations and 10‒25 % higher calculated values of the bending moments in critical sections compared with the results of the classical model of lateral oscillations. The greatest difference between the simulation results was observed with moderate seaways. With a growth of seaways, the difference between the two models decreases. Proceeding from the obtained results, it is not recommended to neglect the effect of variation in time of the forces tensioning the in applied problems of studying operation in conditions of slight sea.