  Spectral density of quantum Ising model in two fields for large but finite
number of spins $N$, is discussed in detail. When all coupling constants are of
the same order, spectral densities in the bulk are well approximated by a
Gaussian function which is typical behaviour for many-body models with
short-range interactions. The main part of the paper is devoted to the
investigation of a different characteristic case when spectral densities have
peaks related with strong degeneracies of unperturbed states in certain limits
of coupling constants. In the strict limit $N\to\infty$, peaks overlap and
disappear but for values of $N$ accessible in numerical calculations they often
strongly influence spectral densities and other quantities as well. A simple
method is developed which permits to find general approximation formulae for
multi-peak structure of spectral density in good agreement with numerics.
