An automatic sawing machine for sawing natural stones pieces and concrete blocks, said machine comprising: i) a frame ; ii) a first conveyor belt and a second conveyor belt , said first conveyor belt and said second conveyor belt being both motorized and mutually arranged at right angles, the first conveyor belt and the second conveyor belt defining in a longitudinal direction (X) a channel-like cutting path suitable to receive consecutive natural stones pieces or concrete blocks (B) to be cut; iii) a plurality of cutting devices , each cutting device comprising a motor on whose shaft a circular blade is keyed, said cutting devices being restrained to said frame subsequent to each other in said longitudinal direction (X) and being arranged above the channel-like cutting path defined by the conveyor belts with respect to a vertical direction (Z), perpendicular to the longitudinal direction (X), so that the respective circular blades are located within the channel-like cutting the path; iv) a positioning device configured to maintain said blocks (B) in contact with the conveyor belts that define the cutting path during their processing, wherein that said positioning device comprises a bar restrained to the frame in the longitudinal direction (X) of the automatic sawing machine parallel to the cutting path defined by the conveyor belts , said bar comprising a plurality of arms pivotally restrained thereto and urged away therefrom by way of a respective tensioning device, wherein the bar of the positioning device is mounted movably perpendicularly to the cutting path defined by the conveyor belts , and in that the conveyor belts are mounted movably relative to the frame and wherein said automatic sawing machine further comprises a plurality of guiding members arranged between pairs of circular blades that are consecutive to each other in the longitudinal direction (X), wherein each guiding member comprises a support fixed to the frame of the automatic sawing machine in the zone comprised between two consecutive cutting devices and a sheet metal plate lying on the same plane of the circular blades , said sheet metal plate extending in the vertical direction (Z) and progressively widening in the longitudinal direction (X) from said support , the overall configuration of the guiding member being such that the sheet metal plate forms together with the circular blades a surface that is substantially continuous in the longitudinal direction (X).. i) a frame ; ii) a first conveyor belt and a second conveyor belt , said first conveyor belt and said second conveyor belt being both motorized and mutually arranged at right angles, the first conveyor belt and the second conveyor belt defining in a longitudinal direction (X) a channel-like cutting path suitable to receive consecutive natural stones pieces or concrete blocks (B) to be cut; iii) a plurality of cutting devices , each cutting device comprising a motor on whose shaft a circular blade is keyed, said cutting devices being restrained to said frame subsequent to each other in said longitudinal direction (X) and being arranged above the channel-like cutting path defined by the conveyor belts with respect to a vertical direction (Z), perpendicular to the longitudinal direction (X), so that the respective circular blades are located within the channel-like cutting the path; iv) a positioning device configured to maintain said blocks (B) in contact with the conveyor belts that define the cutting path during their processing, <EOS>