  We study the properties of the probability density function (PDF) of a
bistable system driven by heavy tailed white symmetric L\'evy noise. The shape
of the stationary PDF is found analytically for the particular case of the
L\'evy index \alpha = 1 (Cauchy noise). For an arbitrary L\'evy index we employ
numerical methods based on the solution of the stochastic Langevin equation and
space fractional kinetic equation. In contrast with the bistable system driven
by Gaussian noise, in the L\'evy case the positions of maxima of the stationary
PDF do not coincide with the positions of minima of the bistable potential. We
provide a detailed study of the distance between the maxima and the minima as a
function of the potential's depth and L\'evy noise parameters.
