A cryogenic system is described for boring a small-diameter hole through various materials including rock, soil and stone. It employs a valveless technique in a borehead [3000] where cryogenic fluid [7] fills at least one pulsejet [3100] which has proximal [3001] and distal [3003] ends. The cryogenic fluid [7] is frozen into a plug [8] near the distal end [3003], acting as a valve. Cryogenic fluid [7] just distal to the frozen plug [8] is rapidly heated by thermal units [3510, 3530] causing it to become a rapidly-expanding gas bubble. The rapidly-expanding gas bubble forces any liquid [7] distal to the expanding gas out of the distal end [3003] of each pulsejet [3100] causing it to impact the material [I]. Rapidly repeating this process causes the system to bore a hole through the material [I].