Abstract. The numerical modeling of the process of two-dimensional axisymmetric flow of combustion gases in the chamber of a liquid rocket engine is considered in this study. In general, when solving such problems, meshes are used which lines coincide with the boundaries of the computational domain. However, an alternative solution is proposed here, which is to apply the extended cells method. It allows using rectangular Cartesian grids, which lines do not coincide with the boundaries of the computational domain, without reducing the stability of the numerical solution due to the fractional finite volumes. This also simplifies the setting of boundary conditions in such volumes. The advantage of the proposed approach over the generally accepted one is the absence of the global geometric transformations during the entire modelling process, which leads to a reduction in its duration. To perform the numerical modelling, an inviscid ideal compressible gas of constant chemical composition was chosen as a basic model of a continuum. It is described by a system of the unsteady Euler equations in integral form, which was closed by the Mendeleev-Clapeyron equation of state. For the numerical solution of this system, the finite volume method was used with the reconstruction of the flow parameters by the WENO algorithm of the third order of accuracy. The solution of the Riemann problem was carried out using the Lax-Friedrichs relations. Time integration of the system of equations was performed using the explicit Runge-Kutta method of the third order of accuracy. All calculations were carried out on a uniform rectangular Cartesian mesh, which lines did not coincide with the boundaries of the computational domain. The results were compared with the solution of the same problem using the ANSYS Fluent on an unstructured mesh coinciding with the boundaries of the computational domain. The value of the relative error obtained as a result of comparing both solutions did not exceed 0.05.