A tool positioning device and a machining element have simple structures which can reduce running cost. In addition to a hole that engages with a shank of an end mill, a channel is provided so that it penetrates through the device such that one end thereof communicates with an upper face of the device and the other end communicates with a lower end of the device. In this case, it is more effective to provide a concave portion that is opened to the upper face and communicates with the hole. The same effect may be obtained by making a cylindrical hole, for example, instead of the channel.