  We apply the Regge-Wheeler formalism to study axial and polar gravitational
waves in Kantowski-Sachs universe. The background field equations and the
linearised perturbation equations for the modes are derived in presence of
matter. To find analytical solutions, we analyze the propagation of waves in
vacuum spacetime. The background field equations in absence of matter are
solved by assuming the expansion scalar to be proportional to the shear scalar.
Using the method of separation of variables, the axial perturbation parameter $
h_0(t, r) $ is obtained from its wave equation. The other perturbation $ h_1(t,
r) $ is then determined from $ h_0(t, r) $. The anisotropy of the background
spacetime is responsible for the damping of the axial waves. The polar
perturbation equations are much more involved compared to their FLRW
counterparts, as well as to the axial perturbations in Kantowski-Sachs
background. In both the axial and polar cases, the radial and temporal
solutions separate out as products. The temporal part of the polar perturbation
solutions are plotted against time to obtain an order of magnitude estimate of
the frequency of the propagating GWs and lies in the range 1000-2000 Hz. Using
standard observational data for the GW strain we have placed constraints on the
parameters in the polar perturbation solutions. The perturbation equations in
presence of matter show that the axial waves can cause perturbations only in
the azimuthal velocity of the fluid without deforming the matter field. But the
polar waves must perturb the energy density, the pressure and also the
non-azimuthal components of the fluid velocity.
