The elastic properties of as-deposited high-purity micron-thick polycrystalline Al and Ag films were measured with the double paddle resonator technique down to 6 mK, and important differences from previous measurements were found. The lowest internal frictions (Q-1) observed were 3× 10-5 in Al and 4× 10-5 in Ag, indicating that these films can contribute substantially to the damping of mechanical resonators, even at very low temperatures. In Al, we also observed agreement between the relative change in sound speed δv/ v0 and Q-1 and the predictions of the tunneling model for an amorphous superconductor well below Tc. Dislocation kinks tunneling between local minima in a kink-Peierls potential modulated by disorder could form the broad distribution of tunneling states required by the tunneling model. However, previous measurements have shown that the thermal conductivity, heat capacity, and heat release of polycrystalline bulk metal and films are not in agreement with the tunneling model predictions. © 2010 The American Physical Society.