We consider the numerical simulation of multi-body contact problems in linear elasticity. For the discretization of the transmission conditions at the interface between the bodies by means of a transfer operator nonconforming domain decomposition methods (mortar methods) are used. Here, we focus on the difficulties related to the discrete choice of the transfer operator. We explain in detail how the transfer operator can be implemented in the case of three-dimensional nonplanar contact boundaries. For the numerical solution of the arising nonlinear systems of equations monotone multigrid methods are used, which do not require any regularization of the nonpenetration condition at the contact interface.