  A lattice model of radiative decay (so-called spin-boson model) of a two
level atom and at most two photons is considered. The location of the essential
spectrum is described. For any coupling constant the finiteness of the number
of eigenvalues below the bottom of its essential spectrum is proved. The
results are obtained by considering a more general model $H$ for which the
lower bound of its essential spectrum is estimated. Conditions which guarantee
the finiteness of the number of eigenvalues of $H,$ below the bottom of its
essential spectrum are found. It is shown that the discrete spectrum might be
infinite if the parameter functions are chosen in a special form.
