In this paper, we propose an extension of the vehicle routing problem with cross-docking that takes into account resource constraints at the cross-dock. These constraints limit the number of docks that can be used simultaneously. To solve this new problem, we adapt a recently proposed matheuristic based on large neighborhood search. In particular, we focus on the feasibility tests for insertions and compare heuristics and constraint programming strategies. Finally, computational experiments on instances adapted from the vehicle routing problem with cross-docking are reported. They give insights on the impact of a limited cross-dock capacity on the routing cost.