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In many clusters of galaxies, X--ray observations have established that large quantities of gas are cooling below X--ray emitting temperatures. Determining the final state of this material remains one of the fundamental questions facing the cooling flow scenario. The detection by White et. al (1991) of excess X--ray absorption in a sample of cluster cooling flows may represent one solution to this quandary. These observations imply the presence of $10^{11}$--$10^{12} M_{\odot}$ of cold, absorbing material and may represent the first direct evidence for the accumulated cooling material. To assess the impact of this cold material, we have calculated the emergent X--ray properties for a set of models including the photoelectric opacity due to accumulated cold material. These models are steady--state, spherically symmetric, and exhibit inhomogeneous gas distributions with material cooling out of the flow over all radii.
Including the opacity due to accumulated cold material reduces the
central X--ray surface brightness profile substantially, with
decreases between 40\%--80\% for radii less than 10 kpc.
The total X--ray luminosity is decreased by $\sim$25\% (0.1--10 keV)
assuming 100\% of the cooling material goes into this cold, X--ray
absorbing form.
This result implies that derived values for the total cooling rate
$\dot M_X$ may be underestimated if opacity effects are neglected.
In addition, significant amounts of cold, X--ray absorbing material
produce steeper deconvolved mass deposition profiles.
We find that models with higher mass deposition in the central regions
can produce profiles comparable to the $\dot M(
