An analysis to determine shear centers for anisotropic elastic thin-walled composite beams, cantilevered and loaded transversely at the free end is presented. The shear center is formulated based on familiar strength of material procedures analogous to those for isotropic beams. These procedures call for a balancing of torsional moments on the cross sectional surface and lead to a condition of zero resultant torsional couple. As a consequence, due the presence of anisotropic coupling, certain non-classical effects are manifested and are illustrated in two example problems. The most distinguishing result is that twisting may occur for composite beams even if shear forces are applied at the shear center. The derived shear center locations do not depend on any specific anisotropic bending theories per se, but only on the values of bending and shear stresses which such theories produce.