  The static and dynamic electric-dipole polarizabilities and tune-out
wavelengths for the ground state of Cs atoms are calculated by using a
semiempirical relativistic configuration interaction plus core polarization
approach. By considering the hyperfine splittings, the static and dynamic
polarizabilities, hyperfine Stark shifts, and tune-out wavelengths of the
hyperfine components of the ground level of $^{133}$Cs atoms are determined. It
is found that the hyperfine shifts of the first primary tune-out wavelengths
are about $-$0.0135 nm and 0.0106 nm, which are very close to the hyperfine
interaction energies. Additionally, the contribution of the tensor
polarizability to the tune-out wavelengths is determined to be about $10^{-5}
\sim 10^{-6}$ nm.
