A drilling system for drilling vertical holes in a mine roof includes a chuck configured to be driven in rotation by a motorized drill head. The chuck is cylindrical has a bore having a first polygonal inside perimeter. A drill member has an elongated hollow body with a cross section defining a circular outside perimeter over most of its length and a constant, second polygonal inside perimeter along substantially the entire length of the drill member. The drill member has at least one end region having a first polygonal outside perimeter that is sized to fit into the first polygonal inside perimeter to rotationally engage the drill member with the chuck. Drill bits having a bit fixture having a cross section with a second polygonal outside perimeter are sized and configured to fit snugly inside the second polygonal inside perimeter to be mounted to the drill member opposite the chuck.