Residual velocity dispersion in cold dark matter induces stresses which lead to effects that are absent in the idealized dust model. A previous Newtonian analysis showed how this approach can provide a theoretical foundation for the phenomenological adhesion model. We develop a relativistic kinetic theory generalization which also incorporates the anisotropic velocity dispersion that will typically be present. In addition to density perturbations, we consider the rotational and shape distortion properties of clustering. These quantities together characterize the linear development of density inhomogeneity and we find exact solutions for their evolution. As expected, the corrections are small and arise only in the decaying modes, but their effect is interesting. One of the modes for density perturbations decays less rapidly than the standard decaying mode. The new rotational mode generates precession of the axis of rotation. The new shape modes produce additional distortion that persists during the subsequent (linear) evolution, despite the rapid decay of the terms that caused it.