Machine for flaring holes in diaphragms of heat exchangers, comprising: - a first ground support frame, having a main direction of extension (x), adapted to support a diaphragm on a plane (41, 42); - a first working head, comprising a first flaring tool, provided with rotation movement around its vertical axis, and vertical translation means for said first flaring tool; - a second frame adapted to support said first working head so that the latter is mobile with respect thereto; - motor means for driving said machine; - a control unit, wherein said first working head comprises tilting means for said first flaring tool, adapted to allow an angular deviation movement with respect to a hub belonging to the vertical axis of rotation of said first flaring tool, when said first flaring tool touches said diaphragm to be inserted into one of said holes, characterized in that said machine comprises a second working head comprising: - a second flaring tool provided with rotation movement around its vertical axis and vertical translation means for said second flaring tool; - tilting means for said second flaring tool adapted to allow an angular deviation movement with respect to a hub belonging to the vertical axis of rotation of said second flaring tool, when said second flaring tool touches said diaphragm to be inserted into one of said holes, wherein said second working head is situated on the opposing side with respect to said first working head and to said plane. - a first ground support frame, having a main direction of extension (x), adapted to support a diaphragm on a plane (41, 42); - a first working head, comprising a first flaring tool, provided with rotation movement around its vertical axis, and vertical translation means for said first flaring tool; - a second frame adapted to support said first working head so that the latter is mobile with respect thereto; - motor means for driving said machine; - a control unit, wherein said first working head comprises tilting means for said first flaring tool, adapted to allow an angular deviation movement with respect to a hub belonging to the vertical axis of rotation of said first flaring tool, when said first flaring tool touches said diaphragm to be inserted into one of said holes, characterized in that said machine comprises a second working head comprising: - a second flaring tool provided with rotation movement around its vertical axis and vertical translation means for said second flaring tool; - tilting means for said second flaring tool adapted to allow an angular deviation movement with respect to a hub belonging to the vertical axis of rotation of said second flaring tool, when said second flaring tool touches said diaphragm to be inserted into one of said holes, - a second flaring tool provided with rotation movement around its vertical axis and vertical translation means for said second flaring tool; - tilting means for said second flaring tool adapted to allow an angular deviation movement with respect to a hub belonging to the vertical axis of rotation of said second flaring tool, when said second flaring tool touches said diaphragm to be inserted into one of said holes, wherein said second working head is situated on the opposing side with respect to said first working head and to said plane.