This paper presents a non-destructive evaluation method of volumetric texture using resonant ultrasound spectroscopy (RUS). It is based on a general theoretical platform that links the directional wave speeds of a polycrystalline aggregate to its texture through a simple convolution relationship, and RUS is employed to obtain the speeds by measuring the elastic constants, where well-established experimental and post-processing procedures are followed. Important lower-truncation-order textures of representative hexagonal and cubic metal samples with orthorhombic sample symmetries are extracted, and are validated against independent immersion ultrasound and neutron tests. The successful deployment of RUS indicates broader applications of the general methodology.