A grinding machine for the grinding or rasping of rubber items having a conveyor belt (1) which feeds the rubber items in under a grinding cylinder (3). Under the conveyor belt (1) in the area under the grinding cylinder (3), at a distance from and freely moveable--within determined limits--there is mounted a support surface (14) which seeks to press the surface (14) in the direction towards the grinding cylinder (3). The support can be, for example, of one or more bellows cylinders (13) which provide central support for the surface (14). The pressure in the bellows cylinder is formed by compressed air from a compressed-air pipe (23) with a substantially constant pressure. Under the conveyor belt a pivotably mounted (7) guide plate (6) is provided, the one side of which is linked to the support surface (14) via a hemispherical surface (12), which, via a strap or an angle piece (9), is secured to the support surface (14).