A casing for a turbine engine compressor, including: cavities in a thickness of the casing, extending in parallel to one another from an inner face of the casing along a circumference thereof, the cavities not being in communication with one another. The cavities, which are elongate and extend along a main direction of orientation between two side walls, are closed upstream and downstream by upstream and downstream faces respectively, and an upstream border and a downstream border are formed at the intersections between same and the inner face of the casing. The upstream border of the cavities takes a form of a wavy line including at least two alternate undulations over a length thereof between the side walls.