Method for manufacturing cervical prostheses with a concavity after grinding, having the following steps: positioning a grinding tool (2) in a resting position (X0, Z0), loading the part (1) to grind, displacing the grinding tool (2) relative to the part (1) to grind along an axis (Z) parallel to the tool's rotation axis, displacing the grinding tool (2) relative to the part (1) to grind along an axis (X) perpendicular to the tool's rotation axis, so as to bring the tool in grinding start position, grinding the concavity (100) by combining rotation movements of the grinding tool and rotation movements of the part (1) around the two axes (Z, C) parallel to each other.