In this contribution, we introduce a generic and parallel AMR strategy for solving 3D contact mechanics problems on hexahedral elements. In order to carry out simulations, we place ourselves in the MFEM software [1] environment, an open-source finite elements method library. The proposed scalable contact algorithm is first based on a mesh partitioning that guarantees the contact paired nodes to be on the same processes. The combined AMR-contact algorithm is ruled by two nested iterative loops. The external loop concerns the AMR process while the internal one deals with the contact solution. The contact is treated by a node-to-surface algorithm with a penalization technique and is solved thanks to a dedicated iterative solver. Once the contact loop converged, the AMR strategy is locally applied and the mesh decomposition is rebalanced with the previously discussed partitioning contact constraints. For the AMR process, a non-conforming h-adaptive mesh refinement solution is considered. This method has already shown high scalability [1]. Super-parametric elements are used to preserve the shape of hierarchically refined geometries, even for first-order finite element solutions. In MFEM, the currently implemented h-adaptive method is enriched with our own estimate-mark-refine approach based on recent works [2]. The proposed AMR-HPC strategy has been successfully confronted for thousands of cores with academic and industrial elastostatics test cases with tens of millions of unknowns.