The density gradient (DG) model is tested for its ability to describe tunneling currents through thin insulating barriers. Simulations of single barriers (MOS diodes, MOSFETs) and double barriers (RTDs) show the limitations of the DG model. For comparison, direct tunneling currents are calculated with the Schrodinger-Bardeen method and used as benchmark. The negative differential resistance (NDR) observed in simulating tunneling currents with the DG model turns out to be an artifact related to large density differences in the semiconductor regions. Such spurious NDR occurs both for single and double barriers and vanishes, if all semiconductor regions are equally doped.