A tire tread includes a running surface intended to be in contact with the roadway during travel. The running surface has a plurality of first cut-outs of a depth less than the thickness of the tread and defining tread pattern elements of a height less than the total thickness of the tread. The tread has a plurality of cavities located subjacent the running surface when the tread is new. Each of these cavities eventually forms at least one new groove or incision in the running surface after partial wearing of the tread. Each cavity is delimited by the rubber of the tread and has an upper generatrix beneath the running surface when the tread is new. The upper generatrix of each cavity follows an undulating profile having a series of recesses and elevations, the amplitude of these recesses and elevations being at least 10% of the depth of the new grooves or incisions that are eventually created.