The full elastic tensor of orthorhombic dysprosium scandate (DyScO(3)) at room temperature was determined by resonant ultrasound spectroscopy (RUS). Measurements were performed on three 500 μm thick substrates with orientations (110), (100) and (001) in the Pbnm (a < b < c) setting. For this purpose, a modification of the RUS method was developed, enabling simultaneous processing of the resonant spectra of several platelet-shaped samples with different crystallographic orientations. The obtained results are compared with ab initio calculations and with elastic constants of other rare-earth scandates, and are used for discussion of the in-plane elasticity of the (110)-oriented substrate.