The unproperly control of friction force between the electrode wire and director tends to break the electrode wire and exacerbate the vibration of electrode wire in the electrical discharge micro-hole machining. In the light of this problem, the electrode wire is simplified to the Euler-Bernoulli beam to establish the calculation model of the critical friction force and analysis model of its inherent mode. The law between the electrode wire’s length and the friction’s influence on the natural frequency of the transverse vibration of the electrode wire is analyzed by using the finite element method. The critical frictional force of electrode wire with a diameter of 0.19 mm is calculated. The critical speed of the micro-feed rotary axis is further determined. The conclusion can be used to guide the selection and optimization of process parameters in the process of electrical discharge micro-hole machining.