AbstractA finite element formulation is presented for treatment of the mechanical interaction between a rod‐like object and a continuous medium, as occurs, for example, between reinforcing steel and surrounding concrete. An impenetrability constraint restricts the rod's lateral motion relative to the continuum, while an accompanying constraint allows axial slip subject to a release criterion. Satisfaction of these constraints is enforced via application of penalty and augmented Lagrangian regularizations. The proposed implementation is suitable for both static and dynamic implicit equation solving schemes, making it useful for a wide range of problem