Аннотация:The paper is devoted to the study of a rarefied gas flow through a finite length conical pipe into vacuum.The problem is solved in the complete geometrical setup, which included not only the pipe, but alsohigh- and low-pressure reservoirs. The analysis is based on the direct numerical solution of the Boltzmann kinetic equation with the S-model collision integral in three space dimensions. The method of thesolution is based on the recent implicit total variation diminishing (TVD) method on unstructured spatialmeshes. It is conservative with respect to the collision integral and work across all flow regimes. Theresults are provided for various ratios of the outlet and inlet diameters, pipe’s lengths and Knudsennumbers. The computed flow rates are compared with the case of the circular pipe of constant radius aswell as an approximate method for very long pipes. The influence of the pipe geometry on the flow fieldis also examined. The presented results can be used as a benchmark for calculations by other methodsand codes