Thin-walled parts are susceptible to deformation and chatter in milling due to their low rigidity, which can negatively affect machining quality and efficiency. Deformation induced by cutting force has an impact on chatter stability, making it difficult to predict the stability of the milling system accurately. To address the above issue, this paper presents a systematic study on the force-induced deformation and chatter stability, with a fast method for calculating the deformation and predicting the chatter stability accurately. Firstly, a dynamic model for milling thin-walled part and a finite element model for calculating force-induced deformation were established. The mechanism of the deformation on chatter stability was analyzed. Secondly, a method for quickly calculating the force-induced deformation using a surrogate model of radial basis function neural network was proposed. The model was built using a small amount of finite element simulation data, which can accurately predict the deformation and its distribution. Finally, the chatter stability was predicted by the obtained dynamic parameters and validated by the milling tests. The results indicate that this method can reduce computation time and improve prediction accuracy evidently.