Possibilities for using general-purpose graphics processing units to simulate compressible gas flows are discussed. Consideration is given to different schemes of computation of flows through the faces of the flow control volume and to the features of their implementation on graphics processing units. A solution of a number of model problems of gas dynamics on graphics processing units is presented and consideration is given to approaches to optimization of the program code connected with the use of different types of memory. A comparison is made between the rates of counting on a graphics processing unit and a central processor using grids having different resolution capabilities and various difference schemes of computation of flows.