Based on analysis of the reason of nodal diameter transverse vibration of thin type circular saw in sawing the stone, it was found out that the wave of the wavy deformation of traveling wave on the saw edge led to the additional axial force of sawing force. The mathematical model of axial additional force was deduced by traveling wave theory in a rotating coordinate system with the same rotational speed as the diamond circular saw, and then the transverse vibration model of diamond saw blade was built by using the thin plate theory of elastic mechanics. The model was pretreated by using complex analysis theory and some proper mathematical methods. The solving algorithm for transverse vibration model and the simulation program were designed based on the Newmark method. In order to verify the validity of the model, a transverse vibration monitoring experiment was completed in the stone producing spot. The transverse vibration of two positions of the diamond saw blade was measured under different process parameters. The error between simulation result and experimental result was less than 13%, therefore, the correctness of the model was verified. The established transverse vibration model could provide theoretical support for optimization of saw blade structure, design of sawing machine tool, noise reduction in sawing process and improvement of the machining surface quality.