In a state where a rail drilling machine is attached to a rail, a drive source, a cutter support mechanism, and a support base are arranged on one side of the rail. A support plate having an upper support surface and a lower support surface is provided on either end of the support base in the longitudinal direction. The upper support surface and the lower support surface of each support plate contact a lower surface of the rail head and an upper surface of the rail foot, respectively, so that the support base is prevented from moving vertically with respect to the rail. The support base has a magnetic sticking portion located between the support plates. The magnetic sticking portion has a sticking surface that is stuck to a side surface of the rail web. In a state where the sticking surface of the magnetic sticking portion is stuck to the side surface of the web, the cutter attaching portion of the cutter support mechanism is arranged in such a manner that a rotation axis of the cutter attaching portion extends, on the outer side of the support base, toward the web.