  The tunneling of Gaussian wave packets has been investigated by numerically
solving the one-dimensional Schr\"odinger equation. The shape of wave packets
interacting with a square barrier has been monitored for various values of the
barrier width, height and initial width of the wave packet. Compared to the
case of free propagation, the maximum of a tunneled wave packet exhibits a
shift, which can be interpreted as an enhanced velocity during tunneling.
