The paper presents a constraint-based collision model for Cosserat rods, able to handle dynamic or static contact between a large number of highly flexible structures. The model provides the required collision impulses prior to updating the solution of the rods, with the impulses accounted for as external loads. The procedure avoids the need to modify the structure solver itself and circumvents any iteration between the collision model and the solver for the Cosserat rods, maintaining the efficiency of any chosen Cosserat solver. The collision model is adopted from Tschisgale et al. (Arch. Appl. Mech. 89(2):167–193, 2019) and extended towards higher stability, which is found necessary in the case of very flexible rods. Furthermore, the model is supplemented with additional terms that arise when the colliding rods are immersed in a fluid. The latter is accounted for by an immersed-boundary method. A large number of tests are conducted to demonstrate the functionality of the final model. Beyond the present study, this set of cases may constitute a suitable test bench for dry and wet collisions of flexible structures.