  Hundreds of substellar companions to solar-type stars will be discovered with
the Kepler satellite. Kepler's extreme photometric precision gives access to
low-amplitude stellar variability contributed by a variety of physical
processes. We discuss in detail the periodic flux modulations arising from the
tidal force on the star due to a substellar companion. An analytic expression
for the variability is derived in the equilibrium-tide approximation. We
demonstrate analytically and through numerical solutions of the linear,
nonadiabatic stellar oscillation equations that the equilibrium-tide formula
works extremely well for stars of mass <1.4 Msun with thick surface convection
zones. More massive stars with largely radiative envelopes do not conform to
the equilibrium-tide approximation and can exhibit flux variations $\ga$10
times larger than naive estimates. Over the full range of stellar masses
considered, we treat the oscillatory response of the convection zone by
adapting a prescription that A. J. Brickhill developed for pulsating white
dwarfs. Compared to other sources of periodic variability, the ellipsoidal
lightcurve has a distinct dependence on time and system parameters. We suggest
that ellipsoidal oscillations induced by giant planets may be detectable from
as many as ~100 of the 10^5 Kepler target stars. (Abridged)
