In a two-inertia motor system with flexible shaft, a torsional vibration is often generated, as a quick speed response close to the primary resonant frequency is required. This vibration makes it difficult to achieve a quick response of speed and disturbance rejection. This paper provides an autonomous pole assignment technique for three kinds of speed controllers (I-P, I-PD, and State feedback) using GAs(Genetic Algorithms) for a two-inertia motor system. Firstly, the optimal parameters are chosen using GAs in view of reducing overshoot and settling time, then those are used in computing the gains of each controller. Some simulation results verify the effectiveness of the proposed design. The proposed controller is expected to be the standard for controlling a two-inertia motor system with flexible shaft.