Abstract: The present invention is concerned with a method and an apparatus for cutting a stone based material of which product can conveniently be used in the form of a tile or the like employable for constructing a walking road, a building floor, a building wall or the like.First, a lower elastic plate having a lower cutting wire formed thereon to exhibit a desired contour is placed on a platform for the cutting apparatus at a predetermined position, and thereafter, a stone based material to be cut is placed on the lower cutting wire of the lower elastic plate. Subsequently, an upper elastic plate having an upper cutting wire formed thereon to exhibit the same or the substantially same contour as that of the lower cutting wire is fixed to the moving part of a press section for the cutting apparatus at a predetermined position positionally coincident with the foregoing predetermined position on the lower elastic plate.