In this paper, we demonstrate that the neglect of elastic end effects, usually justified by appealing to Saint-Venant’s principle, cannot be applied routinely in problems involving composite materials. In particular, for fiber reinforced composites, the characteristic decay length over which end effects are significant is, in general, several times longer than the corresponding length for isotropic materials. For plane strain or generalized plane stress of a highly anisotropic transversely isotropic (or orthotropic) material, modeling a fiberreinforced composite, the characteristic decay length is of order b(E/G)^1/2 where b is the maximum dimension perpendicular to the fibers and E, G are the longitudinal Young’s modulus and shear modulus respectively. Thus when E/G is large, as for fiber-reinforced composites, end effects are transmitted over a distance which is of the order of several specimen widths. This is in marked contrast with the situation for isotropic materials where decay lengths of one specimen width are typical. Similar results hold for axisymmetric problems and for sandwich laminates. The results have widespread implications for the mechanics of composite materials.