The underwater robot has gained increasing attention due to the crucial role of oceanographic surveys in monitoring and exploring resources. A bionic underwater robot offers several advantages, including enhanced environmental interaction, reduced noise, improved propulsion, a smaller turning radius, higher efficiency and greater stability. This study designs and investigates a bionic underwater robot featuring undulatory soft fins. Finite element analysis is used to compute the drag and velocity of the robot with various shape designs. Experiments are conducted to measure the velocity under varying design parameters, including kinematic parameters, hull geometric shapes and fin materials. The experimental results reveal that the Type I robot exhibits vertical oscillations that reduce its forward speed. This phenomenon may result from asymmetry between the top and bottom of the stern, generating a pitch moment that leads to lift and causes oscillation. It is also indicated from the experiments that velocity generally increases with amplitude and frequency. The robot achieves optimal velocity performance with a phase difference of 67.5° (0.375π) and an amplitude of 60° for both polyvinyl chloride and natural rubber fins. The robot with Type B at both ends performs better than the one with Type A at both ends, consistent with the finite element analysis results, though the difference is not significant in the current design. The shape design for the hull is crucial and warrants further investigation. This study provides recommendations for optimizing the shape, materials and motion parameters of bionic soft undulating fin underwater robots.