The shape-memory effect is the ability of a material to recover, on heating, apparently plastic deformations that it suffers below a critical temperature. These apparently plastic strains are not caused by slip or dislocation, but by deformation twinning and the formation of other coherent microstructures by the symmetry-related variants of martensite. In single crystals, these strains depend on the transformation strain and can be quite large. However, in polycrystals made up of a large number of randomly oriented grains, the various grains may not deform cooperatively. Consequently, these recoverable strains depend on the texture and may be severely reduced or even eliminated. Thus, the shape-memory behavior of polycrystals may be significantly different from that of a single crystal. We address this issue by studying some model problems in the setting of anti-plane shear.