We examine the effects of optically thick line forces on orbiting circumstellar disks, such as occur around Be stars. For radially streaming radiation (e.g., as from a point source), line forces are effective only if there is a strong radial velocity gradient, as occurs, for example, in a line-driven stellar wind. However, we emphasize here that, within an orbiting disk, the radial shear of the azimuthal velocity leads to strong line-of-sight velocity gradients along nonradial directions. As such, we show that, in the proximity of a stellar surface extending over a substantial cone angle, the nonradial components of stellar radiation can impart a significant line force to such a disk, even in the case of purely circular orbits with no
radial velocity. Given the highly supersonic nature of orbital velocity variations, we use the Sobolev approximation for the line transfer, extending to the disk case the standard CAK formalism developed for line-driven winds. We delineate the parameter regimes for which radiative forces might alter disk properties; but even when radiative forces are small, we analytically quantify higher-order effects in the linear limit, including the precession of weakly elliptical orbits. We find that optically thick line forces, both radial and azimuthal, can have observable implications for the dynamics of disks around Be stars, including the generation of either prograde or retrograde precession in slightly eccentric orbits. However, our analysis here suggests a net retrograde
effect, in apparent contradiction with observed long-term variations of violet/red line profile asymmetries from Be stars, which are generally thought to result from prograde
propagation of a one-arm, disk-oscillation mode. We also conclude that radiative forces may alter the dynamical properties at the surface of the disk where disk winds originate, and in the outer regions far from the star, and may even make low-density disks vulnerable to being blown off completely.