Wear of components is a critical factor influencing the service life of a product. Thus wear prediction and simulation had become an important part of engineering. One of the most common forms of wear in mechanical components is sliding wear. Factors affecting dry sliding wear include normal load, relative speed, geometry (both macroscopic and local or topographic), temperature, environmental and material properties. Sliding wear prediction is done using tribometers. However, such experiments are expensive and time consuming. In the past few decades, a Finite Element Method (FEM) based wear simulation approach has gained popularity. The objective of the present work is the numerical wear prediction of 2D steel-on-steel pin-on-disc dry sliding contact using Finite Element Method (FEM). Initially, the 2D elastic contact problem is solved using non linear finite element method to obtain the pressure at the contact nodes. The contact pressure obtained is validated with the Hertz solution. The Archard's wear law is used along with the Euler's integration scheme to obtain the material worn out at each step. Wear is taken into account by updating the pin geometry after each step. A user defined FORTRAN subroutine UMESHMOTION is used to apply the wear at the contact nodes. Arbitrary Lagrangian-Eulerian (ALE) is used as an adaptive remeshing technique. This technique allows simulating the wear process at each step while maintaining a high quality mesh throughout the analysis. In order to reduce the computational time the extrapolation technique is used. Pin-on-disc experiments are performed using 304 stainless steel as pin material and EN-31 hardened steel as disc material to validate the wear simulation results. The coefficient of friction and the wear coefficient used in the simulations are determined from the experiments. Keywords: Contact Mechanics, Finite Element Method, Wear Prediction, and UMESHMOTION.