The ability of a finite-difference procedure to predict quantitatively the complex flow and combustion process inside a three-dimensional can combustor, is demonstrated. In a typical example presented, a premixed fuel-air mixture is introduced through a concentric annular swirler; secondary combustion air is introduced through a row of six holes on the cylindrical wall. Film cooling air is injected axially through cooling slots at the corner of the diffuser. The procedure involves the numerical solution of 13 simultaneous differential equations in finite difference form. Auxiliary variables, such as temperature, density and other properties, are also computed. Typical results of the computations are presented in terms of velocity profiles, temperature profiles and species concentration profiles. The methd, which has been validated in numerous two- and three-dimensional cases, could be tried by combustor designers.