We have measured qualitative elastic properties of basalt and Berea sandstone from room temperature down to 4 K using Resonant Ultrasound Spectroscopy (RUS). A simple elastic solid should show a monotonic increase in the elastic constants as temperature decreases. The basalt samples show this gross behavior while the sandstone shows a very unexpected anomalous regime between 40 K and 200 K where the elastic constants decrease with decreasing temperature. Both rocks show temperature-dependent structure in both the modulus and internal friction, and also significant hysteresis, indicating history and rate-dependent properties. This data provides insight into the time and energy scales of dynamical effects observed in sandstones. The low temperature range (4 K--300 K) is of interest due to the renewed interest in Mars and Lunar rocks. ¿ 2001 American Geophysical Union