Undulating fin propulsion holds considerable potential in the design of novel underwater vehicles. However, there exist gaps in the understanding of undulating fin propulsion mechanisms, particularly within the context of different numerical strategies. This study aims to evaluate hydrodynamic performance of undulating fin propulsion base on two strategies, namely, the tethered model (TM) and the self-propulsion model (SPM). Specifically, effects of kinematic factors on hydrodynamic performance and wake structures at different conditions are investigated. Importantly, the work presents pros and cons of the two numerical models on evaluating hydrodynamic performance by comparing the simulation results. A result is that there exist different change rules of hydrodynamic parameters even under the same kinematic conditions for the two models. The wake structure in the TM could present three different structures, depending on the traveling wave speed and the inflow speed. However, the wake always presents the 2S-type and thrust-type vortex street in the SPM. The study shows the TM focus on presenting a periodic, fully developed and steady result, but the SPM is more suitable to explore instantaneous hydrodynamic interactions between the flexible body and the developing flow field. The findings offer some insights into understanding the differences between the two models.