Abstract : The presented work in this thesis is devoted to the development of a dynamic model for the an- guilliform swimming suited to the real time control of the future biomimetic "Eel-like robot" of the ROBEA-CNRS project of the same name. The computation of the interactions between a deformable body and the fluid, in which it moves, is a complex problem requiring the integration of the Navier-Stokes equations and the non-linear dynamic equations of the body enduring finished transformations. Pursuing goals of control for robotic, the suggested solution is based on the fusion of two theories : the Slender Body Theory of the fluid mechanic and Cosserat Beam Theory of the solid mechanic. The first theory models the 3-D flow around fish by the stratification "slices by slices" of the 2-D flows and transverse with the principal axis of the animal's body. Basing on the second theory, the fish is modeled by a continuous assembly of rigid sections that represents the animal's vertebrae or the eel-like robot's rigid platforms. On the basis of this model, the purpose of the presented work is to establish the dynamics of the head and the vertebrae of fish in order to work out a numerical algorithm based on the "Newton-Euler formalism". Finally, the obtained simulator works in real time with a good level of precision (i.e. lower than 10%) compared with the numerical computations of the Navier-Stokes equations.