A system for notching tubes to facilitate their joinder to other tubes or rods, in which a first portion of the notch is formed by a rotary cutting action extending progressively inwardly into the tube side wall and then outwardly in an arcuate path, and the second portion of the notch is formed by a plunging, shearing action which simultaneously punches the entire second portion of the notch out of the wall of the tube. The apparatus for forming each of the notches preferably includes a pair of die halves which together define a tube receiving passage intersected by a tool receiving passage, and a cutting tool positioned in the tool receiving passage. The tool is provided with a substantially axially extending rotary cutting edge for forming the first portion of the notch and a shearing edge for punching out the second portion of the notch when the tool is plunged through the wall of a tube positioned in the intersection of the tube and tool receiving passages. In one form of the invention, two sets of tools and dies may be provided for simultaneously shaping both ends of a tube and a conveyor may be provided for carrying the tubes into and removing them from the tool and die sets.