The effect of a tail with non-uniform flexibility on flapping foil dynamics is studied systematically in this work. Both the power extraction and propulsion behaviors of a flapping foil are checked. Three distinct kinds of non-uniform flexibility distribution are considered, i.e., linear distribution, piecewise distribution and heterocercal distribution. Based on the numerical results obtained, it is found that the tail when the flexibility decreasing along the length is beneficial for power extraction, especially for the piecewise distribution. The reason is that the non-uniform flexible tail can generate bigger bending deformation than the uniform flexible tail, which is good for the leading edge vortex (LEV) capture and then results in the significant rise of the lift. On the other hand, the tail with the decreasing flexibility is harmful to the thrust generation, whilst the flexibility increasing along the length has little benefit on propulsion. The results obtained may have implications for the optimization of the flapping foil propeller and energy harvester.