A grinding machine for the flat grinding of construction elements, with - a bearing-machine frame, comprising a rear and a front end part (6a, 6b) and a middle part (6c, L), - a through passage extending through the grinding machine from its rear end to its front end for the construction elements, - a conveying device associated with the through passage for conveying the construction elements through the through passage, - and at least one grinding device, which is arranged with a transverse offset relative to the through passage and can be displaced transversely to and fro within a first transverse guide by a first displacement device, - wherein the grinding device provides a grinding housing and a grinding disc mounted in a rotatable manner within it, - wherein the grinding housing and the grinding disc are each mounted on a transverse slider (13, 17), which is mounted in a manner displaceable to and fro within a transverse guide (12, 16) by a displacement device (11, 15), - and wherein the transverse slider bearing the grinding housing and the transverse slider bearing the gridning disc are each mounted in a manner independently displaceable relative to one another, characterised in that the grinding machine provides more than one grinding device, and the middle part (6c, L) of the grinding machine disposed between the end parts (6a, 6b) is constructed in a modular manner, in that in each case two mutually opposite grinding devices are mounted on a table-like base frame, and as such represent a grinding-station module (70, 72, 73) which is screw connected via the base frame to its adjacent grinding-station module (70, 72, 73) and/or to one end part (6a, 6b). - a bearing-machine frame, comprising a rear and a front end part (6a, 6b) and a middle part (6c, L), - a through passage extending through the grinding machine from its rear end to its front end for the construction elements, - a conveying device associated with the through passage for conveying the construction elements through the through passage, - and at least one grinding device, which is arranged with a transverse offset relative to the through passage and can be displaced transversely to and fro within a first transverse guide by a first displacement device, - wherein the grinding device provides a grinding housing and a grinding disc mounted in a rotatable manner within it, - wherein the grinding housing and the grinding disc are each mounted on a transverse slider (13, 17), which is mounted in a manner displaceable to and fro within a transverse guide (12, 16) by a displacement device (11, 15), - and wherein the transverse slider bearing the grinding housing and the transverse slider bearing the gridning disc are each mounted in a manner independently displaceable relative to one another, characterised in that the grinding machine provides more than one grinding device, and the middle part (6c, L) of the grinding machine disposed between the end parts (6a, 6b) is constructed in a modular manner, in that in each case two mutually opposite grinding devices are mounted on a table-like base frame, and as such represent a grinding-station module (70, 72, 73) which is screw connected via the base frame to its adjacent grinding-station module (70, 72, 73) and/or to one end part (6a, 6b).