We demonstrate a new class of elastic waves in the bulk: When longitudinal and transverse components propagate at the same speed, rolling waves with a spin that is not parallel to the wave vector can emerge. First, we give a general definition of spin for traveling waves. Then, since rolling waves cannot exist in isotropic solids, we derive conditions for anisotropic media and proceed to design architected materials capable of hosting rolling waves. Numerically, we show spin manipulations by reflection. Structures reported in this work can be fabricated using available techniques, opening new possibilities for spin technologies in acoustics, mechanics and phononics.