The geyser phenomenon seriously threatens the safe operation of deep tunnel drainage systems and drop shaft structural safety. To simulate the geyser process in a baffle-drop shaft, a 1:50 scale model test system was used to research the response relationship between the geyser mechanism and test parameters such as water depth, inlet pressure, and inlet volume. The results show that the pressure in a baffle-drop shaft fluctuates sharply during the geyser process. This is caused by the release of a high-pressure air mass, and high-speed movement of the air–water mixture causes a local pressure imbalance in the drop shaft. A prediction formula for the maximum geyser height of a baffle-drop shaft was established by a multiple linear regression model. Geyser occurrence conditions for the baffle-drop shaft were proposed combined with the response relationship between different influence variables and geyser intensity. Except for the inlet pressure, submerged state of the baffles, and measured location, the hydrodynamic load on the bottom of the baffles is also related to the randomness of the air–water mixture jetted on the baffle bottom. The maximum hydrodynamic load on the baffle bottom during the geyser is 10 times the hydrodynamic load on the baffle surface under normal discharge conditions. This research provides a theoretical reference for the structural design and safe operation of baffle-drop shafts.