Acoustoelasticity is an ultrasonic technique which has been used for the determination of active and residual stresses in common structural materials. This paper examines the effect of texture on the acoustoelastic response in polycrystalline bodies. In particular materials which are transversely isotropic aggregates of cubic crystals are studied. The second- and third-order elastic constants of the polycrystal are derived from the elastic properties of the constituent crystals, and the crystalline orientation relative to the body's symmetry axis. The acoustoelastic relations between velocity and deformation are then presented for the aggregate. Finally, evaluation of the acoustoelastic response for several ideal textures using data for aluminum single crystals shows that the response is highly dependent on the texture.