  Rossby waves arise due to the conservation of total vorticity in rotating
fluids and may govern the large-scale dynamics of stellar interiors. Recent
space missions collected huge information about the light curves and activity
of many stars, which triggered observations of Rossby waves in stellar surface
and interiors. We aim to study the theoretical properties of Rossby waves in
stratified interiors of uniformly rotating radiative stars with sub-adiabatic
vertical temperature gradient. We use the equatorial beta-plane approximation
and linear vertical gradient of temperature to study the linear dynamics of
equatorially trapped Rossby and inertia-gravity waves in interiors of radiative
stars. The governing equation is solved by the method of separation of
variables in the vertical and latitudinal directions. Vertical and latitudinal
solutions of the waves are found to be governed by Bessel functions and Hermite
polynomials, respectively. Appropriate boundary conditions at stellar surface
and poles define analytical dispersion relations for Rossby, Rossby-gravity and
inertia-gravity waves. The waves are confined in surface layers of 30-50 $H_0$,
where $H_0$ is surface density scale height, and trapped between the latitudes
of $\pm 60^0$. Observable frequencies (normalized by the angular frequency of
the stellar rotation) of Rossby waves with $m=1$ ($m=2$), where $m$ is the
toroidal wavenumber, are in the interval of 0.65-1 (1.4-2), depending on
stellar rotation, radius and surface temperature. Rossby-type waves can be
systematically observed using light curves of Kepler and TESS stars.
Observations and theory then can be used for the sounding of stellar interiors.
