In an effort to identify new sources of critical raw materials (CRMs) possibility of recovering selected CRMs from Polish coals, chars, and ashes resulting from the combustion of coals and chars was investigated. The samples were collected from pilot fluidized bed gasification systems. The search for CRMs in coal gasification wastes has not been widely reported before. The study used 2 bituminous coal and 1 lignite sample; the concentration of individual critical raw materials (CRMs) was analyzed using the ICP-MS method. The obtained results were compared with Clarke values in coal ash and in the Earth’s crust, and with the adopted cut-off grade. As shown by the analysis, the highest concentrations of CRMs can be found in fly ash, mainly in samples from the eastern part of the Upper Silesian Coal Basin. This applies mostly to Be, Cs, or Sb due to the fact that their concentrations were found to be higher than the Clarke value in the Earth’s crust; the mentioned fly ashes could be used as potential sources of critical elements if appropriate recovery technologies are developed. In addition, the tested materials have elevated Se, Pb, Ni concentrations, but their recovery is currently not economically viable. Compared to the currently adopted cut-off grade levels, there are no critical elements in the analyzed coal gasification waste that could be recovered.