A two-dimensional dynamic model of mantle convection, showing plate-like behavior, is constructed by considering the effects of the previously yielded segments. Only within an uppermost thin layer is the material assumed to yield at a constant stress. The advection of the segments affected by yielding is calculated. The area covered by these segments continues to yield until it reaches a certain depth. The resultant flow shows movement of the top layer in the parameter range in which, without yielding, it becomes sluggish. A comparison of the results with and without historical effects shows the enhancement of the plate-like behavior. We consider the horizontal variation of the yield stress, which may be caused by the difference in the amount of H2O in the crust. The place of sinking is controlled by the lateral change in the yield stress and the flow behavior becomes different from the case with uniform yield stress. ¿ 2000 American Geophysical Union