Scanning electron beam welding (SEBW) is a very important process for welding of thick plates in aerospace, aeronautical and power industries. However, since the invention of this process, the scanning parameters are typically selected through time consuming and costly trial and error. No existing mathematical criterion can be used to select the optimal parameters due to lack of physical understanding of the welding process. In this study, we developed a three-dimensional mathematical model of SEBW capable of modeling the coupled keyhole and weld pool dynamics for the first time, and used it to understand the underlying physics of the welding process and explore the process optimization criterion of circular mode beam scanning by combining welding experiments and modeling. We showed that beam scanning may not always stabilize the keyhole and weld pool, and may not improve the final weld quality of electron beam welding. However, beam scanning can modulate the movement of high temperature positions on keyhole wall, and contribute to a better uniformity of weld pool dynamics behind the keyhole. For circular beam scanning, we proved that low frequency scanning may lead to more welding defects such as porosity, spiking, and spatters because it increases the tendency of keyhole oscillations as compared to the no scanning case. High frequency scanning could stabilize the keyhole to a certain degree and modulate the fluid flow of the weld pool to make it more regular. Additionally, the scanning radius should be neither too small nor too large. Too small radius may lead to more defects, and too large radius can decrease the penetration depth significantly. A dual direction energy uniformity (DDEU) criterion was proposed to select the scanning parameters by considering the energy uniformity degree in the welding direction and the transverse direction. It was demonstrated that process parameters including beam scanning frequency and radius can be successfully optimized using the proposed criterion. (C) 2018 Elsevier Ltd. All rights reserved.