Take one large miner high electric draught shearer for example. According to the lumped mass method, the gear’s moment of inertia of the shearer’s cutting part was equivalent to the gears connecting the output shaft of the electric cutting motor, the stiffness of central shaft and coupling was equivalent to the output elastic shaft of the electric cutting motor, and the dynamic analysis model of the elastic shaft of the cutting part was set up. Based on this model, the lagrange equation was built. The critical speed of the elastic shaft system, the motion situation on main vibration and harmonic vibration mode, motor shaft’s angular displacement, angular velocity, and angular acceleration’s dynamic response process under the condition of step loads were all analyzed and obtained. The critical speed provided theoretical basis for choosing the working speed of every shaft system of the shearer. The hollow elastic shaft had a protective effect to cutting motor’s damping and overload. The research results provided theoretical basis for the design of the elastic shaft of large miner high shearer.