  The relativistic time evolution of multi-layer spherically symmetric shell
systems---consisting of infinitely thin shells separated by vacuum regions---is
examined. Whenever two shells collide the evolution is continued with the
assumption that the collision is totally transparent. The time evolution of
various multi-layer shell systems---comprised by large number of shells thereby
mimicking the behavior of a thick shell making it possible to study the
formation of acoustic singularities---is analyzed numerically and compared in
certain cases to the corresponding Newtonian time evolution. The analytic setup
is chosen such that the developed code is capable of following the evolution
even inside the black hole region. This, in particular, allowed us to
investigate the mass inflation phenomenon in the chosen framework.
