Paper summarizes the first results of two-dimensional (2D) numerically modelled expansion and flow of compressible and non-viscous gas in typical parts of air jet weaving system: in main nozzle designed as an ejector with various shapes of the mixing zone, in relay (auxiliary) nozzle with substantial flow separation in the rash flow bend directly before the nozzle outlet and the influence of the shape of the reed dent edges on the free stream reflection and penetration through reed gaps along a real “porous” wall. Used Euler's equations are solved by a Finite Volumes Method (FVM) with automatic mesh generation and optimization of unstructured triangle mesh. Graphical results show 2D isolines of all state values of the gas, further Mach number, entropy and velocity vectors. ID profiles of all quantities along choosen cross-section or surface can be obtained, too. They give to the designer a large and quick review about the problem. The coincidence with experiment, measuring and real weaving tests is very good. The advantage of the PC using consists in the very quick, simple and user-friendly operation.