Instead of solving the nonlinear differential equation which governs the compressible flow, an approximate method of solution by means of the variational method is used. The general problem of steady irrotational flow past an arbitrary body is formulated. Two examples were carried out, namely, the flow past a circular cylinder and the flow past a thin curved surface. The variational method yields results of velocity and pressure distributions which compare excellently with those found by existing methods. These results indicate that the variational method will yield good approximate solution for flow past both thick and thin bodies at both high and low Mach numbers.