The certificated airplane transport pilot, the pilot-in-command and instructor pilot, was conducting company training with two captain candidates. The second-in-command, a dual student, was flying from the left seat. The instructor requested a no flap, single engine circling approach, which requires that the landing gear not be extended until a safe landing is assured. The landing gear warning horn did not sound due to the position of the flaps and engine power levers. The student made a checklist call out at a time in the landing sequence that occurs after the landing gear is lowered. Neither pilot recalled calling for the landing gear down. The instructor recalled noting that the student did not call for gear down. He stated that he was giving the student an opportunity to lower the gear without being prompted to do so. The airplane contacted the runway with the landing gear up, causing substantial damage. The three pilots were not injured.