The present invention concerns a rotating electrical machine, comprising: a magnetic mass (2), in particular a rotor, comprising first housings (3), a plurality of permanent magnets (11) inserted into the first housings (3), and shims (20), preferably deformable, inserted into the first housings (3) and/or into second housings (12) provided in the magnetic mass (2), the shims (20) being configured to wedge the magnets (11) in the first housings by plastic and/or elastic deformation.