To investigate the role of the amplitude of an object under the unsteady wall effect in fluid dynamics, we modelled an undulating fin near a wall in a two-dimensional Cartesian coordinate system. The fin was tethered in a uniform flow and controlled by a user-defined function program. The unsteady wall effect improved the propulsion force and propulsion efficiency at different amplitudes, but the lift force behaved differently. We determined the critical amplitude for the model, below which the lift force is positive within an appropriate off-wall distance range. At amplitudes larger than the critical amplitude and as the off-wall distance decreases, the average lift force is, however, always negative, causing the undulating fin to overturn towards the wall and lose stability. The essence of propulsion and lift variation lies in the change in the shape of the space between the wall and the fin, which affects the fluid flow structure and pressure distribution. In addition, some interesting phenomena related to the vortex core arrangement and pressure distribution were introduced at different amplitudes caused by the unsteady wall effect. The present results may provide new insights into the behaviours of benthic fish, reducing their undulating amplitudes and pitch angles near walls.