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A finite element analysis model is presented in this work by implementing the UMESHMOTION subroutine in the software suite ABAQUS, simulating the sliding wear in a configuration ball-on-flat on an AISI 316L. The model is based on an arbitrary Lagrangian–Eulerian (ALE) remeshing technique implementing a modified Archard’s equation. In the model, shape functions and Newton–Raphson formulation were implemented to find the contact pressure and sliding values on the sample and thus validate the wear depth with those reported in the literature. A mesh independence analysis was developed, taking into account contact element size, discretization in the total number of cycles, and the maximum step increment. The contact pressure after the initial loading was calculated and compared with values found by Hertzian formulation found in the literature having a maximum error of 8.61%. Wear depth found was in good agreement with the values reported in the literature, with a maximum error of 18.77%.