Wear is an important factor for failures of mechanical components. Current research on wear is mainly focused on experiments while the numerical simulation of wear is hardly used owing to the complexities of the wear process. Explaining the effect of friction on the wear process is important, as it will lead to a deeper understanding of the evolution of wear. This study proposed a numerical method to expound the wear process in the contact between an elastic cylinder and a half-space simulating the ring-block tester. There are two difficulties during the calculation; one is that the contact shapes vary with time, causing the pressure distribution to change simultaneously and the other is the integral equation for calculating the contact pressure under different worn shapes. In the present study, the wear rate was computed using Archard's law and the wear process was calculated step by step until the specified total sliding distance was achieved. During each step of the calculation, the contact topography was updated. The simulation intuitively reproduced the contact state of change from line to surface contact throughout the wear process. Reasonable agreements on the changes of the wear scar, achieved from experiments and numerical simulations, were obtained.