The elastic properties of novel transition metal oxides have been investigated, using a powerful technique known as Resonant Ultrasound Spectroscopy (RUS). Two sets of transition metal oxides have been studied. One is the ruthenate Ca2-xSrxRuO4 series with a layered perovskite structure, a Mott transition system that connects the Mott insulator Ca2RuO4 with the unconventional superconductor Sr2RuO4. The other set contains geometrically frustrated materials, including vanadium spinels AV2O4 (A = Zn, Mn and Fe) and titanate pyrochlores A2Ti2O7 (A= Y, Tb, Yb, Ho and Dy). The elastic response of five Ca2-xSrxRuO4 single crystals (x = 2.0, 1.9, 0.5, 0.3 and 0.2) has been measured. For 2.0 ≥ x ≥ 0.5, a dramatic softening over a wide temperature range is observed upon cooling, caused by the rotational instability of RuO6 octahedra (for x = 2.0 and 1.9) or the static rotation of the octahedra (for x = 0.5). For the Ca-rich samples (x = 0.3 and 0.2), the softening occurs in a very narrow temperature range, corresponding to the structural phase transition from high-temperature-tetragonal to low-temperature-orthorhombic symmetry. Elastic softening in ZnV2O4 is observed near the cubic-to-tetragonal structural phase transition at 50 K. The elastic response of MnV2O4 is quite unusual, displaying a softening over a wide temperature range with decreasing temperature. Upon cooling, C’ of FeV2O4 becomes so soft that it drops to almost zero around 140 K, where the cubic-to-tetragonal structural transition occurs. For Y2Ti2O7, all three elastic constants show normal “Varshni” behavior. For spin liquid Tb2Ti2O7, all three elastic constants show a pronounced softening below 50 K, indicative of a possible Jahn-Teller, cubic-to-tetragonal transition at very low temperatures. It is also found that the application of a magnetic field suppresses the elastic softening in this compound. Another spin liquid Yb2Ti2O7 shows no elastic softening. The elastic moduli of the spin-ice compounds, Ho2Ti2O7 and Dy2Ti2O7, show a broad “dip” around 100 K, which is believed to be caused by the strong crystal field effect in those two compounds.