Abstract The term Schallamach wave is used to describe a wave of detachment that sometimes arises during the frictional sliding of a smooth rubber surface against a smooth rigid surface. Extensive experimental investigations have been made since Schallamach first observed the waves in 1971; however, no successful finite element analysis (FEA) modeling of the behavior has been reported yet. This work uses an explicit dynamics FEA approach to model both the initiation and progression of waves of detachment for the first time. The use of the finite element method allows for the detailed stress and strain analysis at the interface to be examined. Here, the limitations of using a purely elastic solution in plane-strain are explored. To validate the explicit dynamics approach for modeling the Schallamach waves, another biaxial compressive buckling mode has also been modeled.