  We investigate the behaviour of low-mass, planar domain walls in the
so-called $\phi^4$ model of the scalar field on the Schwarzschild and Kerr
backgrounds. We focus on a transit of a domain wall through a black hole and
solve numerically the equations of motion for a range of parameters of the
domain wall and the black hole. We observe a behavior resembling an occurrence
of ringing modes. Perturbations of domain walls vanish during latter evolution,
suggesting their stability against a passage through the black hole. The
results obtained for Kerr and Reissner-Nordstr\"om black holes are also
compared.
