#### Abstract

Within median and/or paired fin (MPF) propulsion, many fish routinely use the long-based undulatory fins as the sole means of locomotion. In this paper, the long-based undulatory fin of an Amiiform fish "G. niloticus" was investigated. A simplified physical model was brought forward, which makes up of N equal thin rods and a rectangular elasticmembrane connecting them together. With light mass, small stiffness and low natural vibration frequency, the long-based fin undulating and fluid loading may induce large flexible distortion of their long-based fins when swimming. 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 in which the geometrical non-linearity of the structure is taken into account. Last, we apply the derived the kinematic model and equilibrium equations of the undulatory fin to analyze the thrust and propulsive efficiency varying with the aspect ratio of the fin and the maximum swing amplitude