Ground milling machine (1) provided with a cover (4), which is mounted across the rotor (3) consisting of milling members situated on a horizontally rotatable shaft (2), which cover is substantially in the form of a half cylinder. A mat (5) made of a flexible material, such as rubber or a like material, is mounted within the cover (4), in which the two end edges (6) of said mat (5) seen in the horizontal direction are situated substantially in front of and behind the shaft (2) of the rotor (3) and extend parallel to it, are fixed to a stiff frame portion (8) and said mat is flexibly and deformably supported between said end edges. The flexible support of the mat (5) is achieved by strips (10) of spring steel mounted in the interior of the mat and extending between its end edges (6), with the ends of said strips being secured to the frame portions (8).