We measured the elastic constants of polycrystalline Y1Ba2Cu3Ox with eleven oxygen contents varying from 6.2 to 6.9. Reported properties include sound velocities; bulk, shear, Young's moduli; Poisson ratio; Debye temperature. After correction to the void-free state, the measurements fail to show a systematic dependence on oxygen content. Focusing on the bulk modulus, all measurements fall below an ionic-crystal model prediction, by 5–50%. We attribute this macroscopic softness to either microcracks or weak grain-boundary mechanical linkages. For the case x = 6.9, we suggest a set of intrinsic elastic constants.