An automatic machine for drilling and milling substantially flat glass sheets shape, comprising includes a machine body; an input conveyor provided with a motorized roller conveyor or roller belt that conveys the glass sheet by its lower edge; an input conveyance surface provided with idle gliding wheels; an output conveyor provided with a motorized roller conveyor or motorized belt that conveys the glass sheet by means of its lower edge; and an output conveyance surface provided with idle gliding wheels. The machine further includes at least one carriage provided with synchronous horizontal motion along the longitudinal axis X2; and at least one pair of working heads provided independently with a synchronous vertical motion for adjustment and feeding along the axes Y1 and Y2, wherein, each head bears a tool provided with rotary motion (cutting) and feeding motion along the axes Z1 and Z2.