Earth dams and levees often offer an attractive habitat for burrowing animals such as porcupines, nutria, badgers, etc. However, their activity may damage the earth structure, potentially leading to catastrophic failures. If the burrow system connects the waterside and the landside, water flows through the pipe and it can start concentrated erosion. This paper shows that the conditions to trigger concentrated erosion can be generated by a local instability mechanism of the landside slope in which the soil cover between the cavity and the surface is expulsed due to increasing water pressure. A simplified model based on the limit equilibrium method is proposed and compared with bi-dimensional and three-dimensional finite element analyses. This mechanism can better explain real failure cases. The results provide useful suggestions for the assessment of levee vulnerability to animal burrows and for the management of water retaining structures.