A numerical method for solving isentropic compressible now problems is presented. This method uses the vorticity and the density as variables. The crux of the method lies in the numerical simulation of the process of vorticity and density variation. The fundamental equation of a compressible discrete vortex method is derived. Unlike the BiotSavart law in the incompressible fluids, the modified Blot-Savart law in compressible fluid should contain the change of the non-solenoidal. The change of density induces the variation of the fluid velocity. The effects of compressibility on flow past a circular cylinder have been investigated by using the compressible discrete vortex method at a Reynolds number of l.E+6. The Mach number is 0.5. The results show that the form of vortex shedding is different from the incompressible now. The separation positions shift upstream, the wake more wide and the street is not clear like the incompressible. A numerical method for solving isentropic compressible now problems is presented. The crux of the method lies in the numerical simulation of the process of vorticity and density variation. The fundamental equation of a compressible discrete vortex Unlike the BiotSavart law in the incompressible fluids, the modified Blot-Savart law in compressible fluid should contain the change of the non-solenoidal. The change of density induces the variation of the fluid velocity. The effects of compressibility on flow past a circular cylinder have been investigated by using the compressible discrete vortex method at a Reynolds number of l.E + 6. The Mach number is 0.5. The results show that the form of vortex shedding is different from the incompressible now. shift upstream, the wake more wide and the street is not clear like the incompressible.