A key role in the decarbonization scenario of industry and energy sectors plays a bio-energy carbon capture technology (BioCCS or BECCS) that results in negative-CO2 power generation. Due to the biological origin of some part of municipal solid waste, the application of carbon capture in waste incineration plants can be classified as BioCCS, and thus, this technology attracted the attention of scientists recently. Currently, there are four incineration plants, in which CO2 capture is implemented; however, they are based on post-combustion technique since it is the most mature method and not requires many changes in the system. Nevertheless, the separation of CO2 from the flue gas stream that contains mostly nitrogen is complex and causes a large drop in the total performance of the system. A better solution from an energy efficiency point of view is the oxy-fuel combustion technology. OFC involves the replacement of air as an oxidizer into high purity oxygen and recirculated exhaust gas. As a result, CO2-rich gas is produced that is practically ready for capture. It is expected that the application of OFC in the incineration plant will cause an increase of temperature of the process and intensify the oxidation of hydrocarbons due to higher oxygen concentration. Moreover, the volume of the flue gas stream will be reduced since there will be an absence of nitrogen. Nevertheless, there is a lack of studies concerning oxy-incineration currently. Therefore, the main goal of the study is to develop a mathematical model of oxy-waste combustion to answer the research questions, such as how the composition of oxidant that is supplied to the process affects the combustion performance. The model includes all important processes taking place within the chamber, such as pyrolysis, char burnout and gas combustion over the grate. The results of the work will contribute to the development of oxy-waste incineration plants and will be useful for design purposes.