Abstract: Rail heads are planed with a mobile machine moving continuously along a track and comprising a frame and a rail planing tool mounting linked to the frame. The mounting is adjusted vertically relative to the running surface of the rail head and pressed thereagainst, and guided along the rail head by a guide roller laterally guiding the mounting along a selected side of the rail head and two additional guide rollers vertically guiding the mounting along the running surface of the rail head. A tool head including a tool holder is mounted on the mounting for displacement relative thereto and a rail planing tool is replaceably mounted in the tool holder and detachably carries a cutting blade having a cutting edge for planing chips or shavings off the rail head by the forward thrust of the machine. A pick-up magnet removes the chips.