Using both measurements and modeling, the elastic and related properties of some oxides and oxide superconductors were studied. The polycrystal elastic constants were measured using a MHz-frequency pulse-echo method between 295 and 4 K and corrected to the void-free state by using a model for a composite material containing spherical particles. The elastic moduli of the high-T(c) superconductor Y1Ba2Cu3O7 (YBCO) were compared with that of oxides, especially the perovskites BaTiO3 and SrTiO3, which are crystal-structure building blocks for the YBCO superconductor. The bulk moduli were also calculated using a Born ionic model with two energy terms: electrostatic (Madelung) and ion-core-repulsion. The calculated bulk modulus of YBCO, 98 GPa, agrees well with measurement, 101 GPa. Based on monocrystal measurements combined with analysis-theory, elastic stiffnesses C(ij) for orthorhombic YBCO were estimated. The bulk modulus obtained from the estimated C(ij) by the Voigt-Reuss-Hill averaging method agrees with the monocrystal measurement. From the measured polycrystalline elastic constants, the Debye characteristic temperatures were calculated.