Micro electrical discharge machining (EDM) has the ability to drill micro holes with high accuracy in metallic materials. The aspect ratio of a micro hole generated by micro EDM is usually higher than those by other processes such as etching, mechanical drilling, and laser. However, it was found that the drilling speed of micro EDM slows down and even stops when the aspect ratio reaches a certain value. To understand this phenomenon, a theoretical model is proposed based on the fluid mechanics and surface tension. Experiments under different machining conditions are carried to verify this model. Experimental results agree with the theoretical values, which indicate the validity of the proposed model. The difference between the theoretical values and the real values might be caused by the debris and the temperature in the discharge gap, which are ignored in the model.