This study was focused on carbonation of waste materials having low water-solubility in which Ca and Mg are generally bound as silicates. Here, pulverized firing oil shale ash (PFA from Narva Power Plants, Estonia), electric arc furnace slag (EAFS, types 1 and 2 from Uddeholm Tooling, Sweden) and ladle slag (LS from Uddeholm Tooling, Sweden) were studied as sorbents for binding CO2 from flue gases in direct aqueous mineral carbonation process. The experiments were carried out at room temperature and atmospheric pressure. Results showed that Ca-Mg-silicate phases bound up to 9 g of CO2 per 100 g of initial ash, which formed 30% of the total CO2 bound in direct aqueous carbonation of PFA. The CO2 uptakes for steel slags (EAFS1, EAFS2 and LS) were 8.7g CO2/100 g EAFS1, 1.9 g CO2/100 gEAFS2 and 4.6 g/100g LS. Quantitative XRD analysis indicated that Ca2SiO4 and Ca3Mg(SiO4)2 were the main CO2 binding low solubility components of oil shale ash as well as steel slags. The main carbonation product was calcite (CaCO3), indicating that Mg-compounds were not reactive towards CO2 at these mild conditions. Based on multifaceted studies on carbonation of oil shale ash, a new method for eliminating CO2 from flue gases by Ca-containing waste material was proposed. The process includes contacting the aqueous suspensions of Ca-containing waste material with CO2 containing flue gas in two steps: in the first step the suspension is bubbled with flue gas keeping the pH levels in the range of 10-12 and in the second step keeping the pH levels in the range of 7-8. The water-soluble components such as free lime are carbonated in the first step and the components of low solubility, in which Ca is generally contained in the form of silicates, are carbonated in the second step.