Mechanical breakdown of graphite materials due to diffusion-induced stress (DIS) is a key aging mechanism of lithium-ion batteries. In this work, electrochemical-thermal coupled model along with a DIS model is developed to study the DIS distribution across the anode thickness. Special attention is paid to the evolution behavior of surface tangential stress (STS) in the discharge process for graphite at different locations of the anode. For the first time, we report that the evolution of STS, as well as local current, at all locations of the anode, evolve like sinusoidal waves in the discharge process with several crests and troughs. The staging behavior of graphite active material, in particular the sharp change of open-circuit potential (OCP) of graphite in the region between two plateaus, is found to be the root cause for the sinusoidal patterns of current and stress evolution. Furthermore, the effects of various parameters, such as starting state of charge, discharge C-rate and electrode thickness on the current and stress evolutions are investigated.