In this paper, a new theory is introduced to explain chatter mechanism based on wave propagation in elastic solids. It is believed that previous theories in chatter are based on a static analysis and normally are consistent just for low-frequency vibrations such as forced vibration. But chatter phenomenon is a dynamic high-frequency event and requires a consistent theory with a dynamic analysis. In this research, variations of inter-stand tensions are calculated based on wave propagation theory. Predicted results by wave propagation theory were evaluated by dynamic finite element method in a benchmark problem. Results show that wave propagation theory is consistent by dynamic finite element method, but previous theories are not sufficiently accurate in chatter conditions. Hereafter, a numerical model is constituted to simulate the vibrational behavior of a tandem rolling mill. Parameters for numerical simulations are adopted from an industrial two-stand tandem mill. Consequently, results of the analytical model are compared with the experimental measurements from that full scale industrial mill. Two main chattering characteristics, i.e., critical rolling speed and chatter frequency, obtained from the simulation program were found to be more consistent with the experimental results when considering the dynamic effects.