Two-dimensional inviscid compressible flows are studied by using Euler equations. One step Lax-Wendroff scheme is utilised for the time marching and finite volume integration technique is applied for the spatial discretisation. The development of the particular finite volume method is presented and von Neumann stability criterion is discussed for the time step selection. The method of characteristics is used to obtain the inlet and outlet boundary conditions. The boundary condition on the solid surfaces is the tangency condition. Three test cases are used to check the validity of the code. These are the subsonic, transonic and supersonic channel flow over a Ni-bump, flow through a supersonic inlet and subsonic, nonisentropic and underexpansion flow regimes in a bell shaped nozzle.