An automatic drilling machine for simultaneously drilling at least two holes through a surface of a crosspiece. The machine comprises an automatic drilling unit having at least two tool holders, each one adapted for receiving a drilling tool. The automatic drilling unit has a cross-shaped channel configured to receive, at least partially, the crosspiece to be drilled inside the automatic drilling unit with. The tool holders are arranged, such as, when the drilling machine is mounted with the crosspiece to be drilled, the tool holders are positioned in accordance with the locations of the crosspiece where a hole is to be drilled.