The fin motion of the manta ray has been an attractive inspiration for biomimetic underwater robot propeller designs. Study shows that the fin of the manta ray generates undulations in both span and chord-wise directions, which is advantageous for speed and agility in swimming. Regarding the undulation generation, the chord-wise undulation (CWU) is relatively challenging to implement. In the existing batoid-inspired robots, the multi-fin-ray driven by individual actuators, like motors or other smart actuators, has been the most common design for the CWU implementation. In this paper, we tap into the viscosity induced motion sequencing for soft fluidic actuators (SFAs) to achieve CWU in a soft fin ray array (SFRA). The SFRA, assembled using eight bi-directional fiber-reinforced SFAs, is hydraulically driven and tested with eight different tubing connection plans for undulation characterization. The results show that the viscosity of water during the flow in the SFRA channel network successfully achieves the undulation along the fin rays with decaying oscillation amplitudes. SFAs with hydraulic actuation are favored candidates for underwater propellers, and this work provides a new solution to the SFA-based biomimetic underwater robot with manta ray like swimming mode.