A rotating electric machine including: —a magnetic mass, in particular rotoric, including first housings, —a plurality of permanent magnets inserted into the first housings, each permanent magnet having two polar faces, and —nonmagnetic shims inserted into the first housings and/or into second housings formed in the magnetic mass, —the shims being configured to cause a deformation of the first housings reducing the parasitic air gap between at least a polar face of a permanent magnet and the corresponding wall of a first housing.