Firstly, the paper established a finite element model for a steel motor shell and computed related modals, vibration velocities, stress and strain respectively. Computational results show that the flange and end shield of the motor shell had the maximum vibration velocities and strain because these locations lacked the reinforcing ribs, while the maximum stress was mainly at joints between different structures. Secondly, the steel material was replaced by the aluminum alloy. Mechanical parameters of the motor shell were recomputed and compared with those of the steel structure. Results show that modal frequency on each order increased, which is good for avoiding the structural resonance. In addition, the maximum stress of the structure decreased by 4.4 MPa, and the maximum strain decreased by 0.27 mm, which could effectively improve the fatigue characteristics of the motor shell under long-term excitation. Then, the boundary element method was used to compute radiation noises of the motor shell in far field, where the radiation noise presented an obvious directivity. Finally, the paper proposed a GA-BP neural network model to predict the radiation noise of the motor and compared the prediction results with the boundary element. In the whole analyzed frequency band, the maximum difference between the neural network prediction and the real values did not exceed 5 dB, indicating that it is feasible to predict radiation noises of the motor by the neural network. Additionally, experiments were also conducted and compared with two kinds of numerical methods. Methods proposed in this paper provide some references for realizing the rapid noise reduction and light weight of motors.