  We investigate the electron-boson spectral density function,
$I^2\chi(\omega,T)$, of CuO$_2$ plane in underdoped
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) and underdoped
YBa$_2$Cu$_3$O$_{6.50}$ (Y-123) using the Eliashberg formalism. We apply a new
(in-plane) pseudogap model to extract the electron-boson spectral function. For
extracting the spectral function we assume that the spectral density function
consists of two components: a sharp mode and the broad Millis-Monien-Pines
(MMP) mode. We observe that both the resulting spectral density function and
the intensity of the pseudogap show strong temperature dependences: the sharp
mode takes most spectral weight of the function and the peak position of the
sharp mode shifts to lower frequency and the depth of pseudogap,
$1-\tilde{N}(0,T)$, is getting deeper as temperature decreases. We observe also
that the total spectral weight of the electron-boson density and the mass
enhancement coefficient increase as temperature decreases. We estimate
fictitious (maximum) superconducting transition temperatures, $T_c(T)$, from
the extracted spectral functions at various temperatures using a generalized
McMillan formula. The estimated (maximum) $T_c$ also shows a strong temperature
dependence; it is higher than the actual $T_c$ at all measured temperatures and
decreases with temperature lowering. Since as lowering temperature the
pseudogap is getting stronger and the maximum $T_c$ is getting lower we propose
that the pseudogap may suppress the superconductivity in cuprates.
