Abstract: Objectives Establish a longitudinal wave glider model, modeling the umbilical cable as multi-segment hinged rigid rods to investigate wave and umbilical parameters' influence on longitudinal motion. Methods Using Lagrange method, develop a multi-rigid-body dynamics model with the umbilical as uniform hinged rods. Calculate wave forces, fluid resistance, and hydrofoil forces. Solve via MATLAB simulation, validating against existing research. Perform sensitivity analysis on parameters. Results The results show that the longitudinal motion response increases with the increase of wave height. When the wave height increases from 0.2 m to 0.4 m, the longitudinal response increases by 78.20 %. With the shortening of the length of the umbilical cable, the longitudinal motion response is enhanced. When the length of the umbilical cable is shortened from 5m to 2m, the longitudinal response increases by 31.97 %. If the wave period is too small, the longitudinal response will be reduced due to the rigid impact between the hinged rigid rods. The change of umbilical cable density has little effect on the longitudinal motion response. Conclusions The research results can provide theoretical support for the structural optimization design and motion control strategy of wave glider.