Many blueschists and eclogites are inferred to have formed from oceanic basalts in subducted slabs. Knowledge of their elastic behavior is essential for reconstructing the internal structure of subduction zones. The Cycladic blueschist unit, exposed on Syros Island (Greece), contains rocks belonging to an exhumed Tertiary subduction complex. They were possibly part of a subduction channel, a shear zone above the subducting slab in which exhumation is possible during subduction. Intense plastic deformation, forming crystallographic preferred orientations (CPO), accompanied blueschist and eclogite metamorphism. CPO of the constituent minerals in the collected samples was determined by time‐of‐flight neutron diffraction. Two samples are foliated fine‐grained blueschists with strong CPO, rich in glaucophane, zoisite, and phengite. Two coarser‐grained eclogite samples rich in omphacite and clinozoisite, or glaucophane, have weaker CPO. Vp and Vs anisotropies were computed from the orientation distribution function and single‐crystal elastic constants. All samples show velocity maxima parallel to the mineral lineation, and minima normal to the foliation, providing important constraints on orientations of seismic anisotropy in subduction channels. Vp anisotropies are up to 3 times higher (6.5–12%) in the blueschists than in the eclogites (3–4%), pointing to a potentially important lithological control of elastic anisotropy in subducted oceanic crust.