the geometric characteristics of the pipe such as i the moment of inertia along the longitudinal axis of the pipe or ei the flexural rigidity a the surface area of the pipe section or ea the axial rigidity l the length of the pipe d the diameter the mechanical characteristics of the pipe such as e the young modulus of the pipe r the lineic weight of the pipe the load applied to the pipe such as the transverse cd and longitudinal cdl drag coefficients interaction of the water on the pipe the model uses the modal decomposition method which is satisfactory for description of the pipe behaviour according to the invention the model is determined by carrying out successively the following operations operation 1 the dynamics of the displacements along the pipe is expressed by the partial differential equations by taking account of the characteristics mentioned above for example the dynamics of the deformations along the pipe in relation to its vertical equilibrium position in plane ox oz is expressed by the following partial differential equations 1 ru u2062 tt u2062 eau u2062 ss u2062 f t r a u2062 w u2062 tt u2062 r s u2062 w u2062 s u2062 t.