A machine for multiple wire cutting of stone material comprising a plurality of cutting devices (4) mounted on a supporting structure (3), each comprising an annular cutting wire (11), driving means (16) for the cutting wire (11), and at least one upper return pulley (17) and one lower return pulley (18) which are vertically distanced from each other on the same side of the machine. The upper pulleys (17) of two adjacent devices (4) are supported respectively by a first part (23) and by a second part (24) of the same upper arm (21) of the supporting structure (3). The lower pulleys (18) of two adjacent devices (4) are supported respectively by a third part (25) and by a fourth part (26) of the same lower arm (22) of the supporting structure (3). The second parts (24) and the fourth parts (26) can also move respectively relative to the first parts (23) and relative to the third parts (25) in such a way as to vary the tensioning of the cutting wire (11) looped around the pulleys mounted on them. Moreover, if the upper pulley (17) of a cutting device (4) is mounted on the first part (23) or respectively on the second part (24) of an upper arm (21), the lower pulley (18) of the same cutting device (4) is mounted on the fourth part (26) or respectively on the third part (25) of a lower arm (22).