The incineration of municipal solid wastes is an important part of the waste management system along with recycling and waste disposal, and the solid residues produced after the thermal process have received attention for environmental concerns and the recovery of valuable metals. This study focuses on the Critical Raw Materials (CRM) content in solid residues from two Italian municipal waste incinerator (MSWI) plants. We sampled untreated bottom ash and fly ash residues, i.e. the two main outputs of common grate-furnace incinerators, and determined their total elemental composition with sensitive analytical techniques such as XRF and ICP-MS. After the removal of a few coarse metallic objects from bottom ashes, the corresponding ICP solutions were obtained using strong digestion methods, to ensure the dissolution of the most refractory components that could host significant amounts of precious metals and CRM. The integration of accurate chemical data with a substance flow analysis, which takes into account the mass balance and uncertainties assessment, indicates that bottom and fly ashes can be considered as a low concentration stream of precious and high-tech metals. The magnesium, copper, antimony and zinc contents are close to the corresponding values of a low-grade ore. The distribution of the elements flow between bottom and fly ash, and within different grain size fractions of bottom ash, is appraised. Most elements are enriched in the bottom ash flow, especially in the fine grained fractions. However, the calculated transfer coefficients indicate that Sb and Zn strongly partition into the fly ashes. The comparison with available studies indicates that the CRM concentrations in the untreated solid residues are comparable with those residues that undergo post-treatment beneficiations, e.g. separation between ferrous and non-ferrous fractions. The suggested separate collection of “fresh” bottom ash, which could be processed for further mineral upgrading, can constitute an attractive option of the waste management system, when physical–mechanical devices are not available or could not be implemented in old MSWI systems. The suggested procedure may lead to the improvement of recovery efficiency up to 83% for CRM and 94% for other valuable metals.