The long-based undulatory fin of an Amiiform fish G.niloticus was investigated. A simplified physical model was brought forward, which was composed of N equal thin rods and a rectangular elastic membrane connecting them together. We established a kinematic model of the long-based undulatory fin on the basis of analyzing the long-based dorsal fin locomotion and considering the fluid-structure interaction. Further, the equilibrium equations of the undulatory fin were obtained by applying the membrane theory of thin shells, which took into account the geometrical non-linearity of the structure. The thrust and propulsive efficiency of the long-based fin undulating can be analyzed by applying the derived kinematic model and the equilibrium equations of the undulatory fin.