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This paper proposes a dynamic model of the swim of elongated fish suited to the online control of biomimetic eel-like robots. The approach can be considered as an extension of the original reactive ldquolarge elongated body theoryrdquo of Lighthill to the 3-D self-propulsion to which a resistive empirical model has been added. While all the mathematical fundamentals have been detailed by Boyer . (http://www.irccyn.ec-nantes.fr/hebergement/Publications/2007/3721.pdf, 2007), this paper essentially focuses on the numerical validation and calibration of the model and the study of swimming gaits. The proposed model is coupled to an algorithm allowing us to compute the motion of the fish head and the field of internal control torque from the knowledge of the imposed internal strain fields. Based on the Newton-Euler formalism of robot dynamics, this algorithm works faster than real time. As far as precision is concerned, many tests obtained with several planar and 3-D gaits are reported and compared (in the planar case) with a Navier-Stokes solver, which, until today have been devoted to the planar swim. The comparisons obtained are very encouraging since in all the cases we tested, the differences between our simplified and reference simulations do not exceed 10%.