In a method and apparatus for cutting expanded graphite sheet material, at least one cutting tool is urged against the sheet(s). The cutting tool has at least one ridge extending therefrom that includes a substantially tapered cross-section having sloping sides and an edge surface. At least a portion of the sheet material is displaced as the ridge is urged against the sheet. A region of the sheet material in contact with the ridge is compressed so that the density of the region reaches or exceeds the breaking density of the sheet.