An anterior part of a nacelle of an aircraft propulsion unit having an air inlet lip at the front end, an internal structure and an external panel extending the air inlet lip, and an annular rigidifying frame having an external peripheral edge connected to the external panel is disclosed. The anterior part of the nacelle includes a shock-absorbing element connected rigidly on the one hand to an internal peripheral edge of the rigidifying frame and on the other hand to the internal structure.