The invention relates to a method of cutting thin laminae of stone, e.g. marble, which comprises bonding a backing layer to the opposed faces of a slab of stone, supporting the slab with backing layers attached, in an upward position on its edge, cutting the slab along a cutting plane parallel to and midway between the opposed faces of the slab to a depth which is about half the depth of the slab, tumbling the slab on to its opposite longitudinal edge, and cutting through the remainder of the depth of the slab to leave a lamina of stone adhered to each backing layer. The invention also includes apparatus for carrying out the aforesaid method, comprising a saw having two disc blades, a bogie movable beneath the saw and having a pair of vacuum-operated slab-gripping devices each of which is adapted to support a slab upwardly on its edge, and a second bogie movable in a direction transverse to the first bogie and carrying means for tumbling a slab supported on one longitudinal edge, through 180.degree., so that it rests on its opposite longitudinal edge.