We study theoretically the few-body dynamics of atoms which leak out of a trap by tunneling through a thin
barrier. We consider the two cases of bosons with strongly repulsive contact interactions and spinless fermions
with strongly attractive contact interactions Bose and Fermi Tonk-Girardeau gases, respectively. The tunneling
is studied as a function of the number of particles N and the barrier opacity. The fermionic case reproduces
a nonexponential decay of a single particle, but with a signal enhanced by a factor of N. In the bosonic case,
we find a different regime of nonexponential decay due to the contribution of different resonances of the trap.
The relevant physical realization is that of atoms confined to an optical box with an end-cap laser barrier, and
the prospects for future experiments are discussed.