We have used resonant ultrasound spectroscopy to measure the three independent elastic constants of Pd-H, Pd-D, and Pd-T single crystal at 300K as a function of hydrogen, deuterium, and tritium concentration, respectively. The addition of interstitial H (D, or T) atoms, located at (0,½,0) in the fcc Pd lattice, affects all three elastic constants C', C44, and B. In the mixed (+) phase, and with increasing H isotope, the shear modulus C' shows an abnormal softening whereas C44 and B do not. This is explained in terms of Zener-type an elastic relaxations affecting the shape of the hydride phases in the coherent(+) two-phase mixture In the single -phase, C' shows a strong isotope dependence whereas C44 and B show none. This behavior is explained in terms of differences in the excitation of optical phonons. In Pd-T, 3He is produced by the radioactive decay of tritium. We have measured in situ the swelling and the change in the elastic constants in Pd-T as a function of aging time. Aging (3He formation) affects all three elastic constants. These measurements are being used to understand the early stages of 3H-3He cluster formation in aged Pd-T crystal.