Abstract Using the direct method of Rayleigh-Ritz in the calculus of variations, the problem of steady irrotational compressible flow past a body of revolution of arbitrary shape is formulated. In order to compare with the analytical solutions obtained by other investigators, two numerical examples have been carried out, namely, compressible flows past a sphere, and an ellipsoid of revolution. The results are found to be in excellent agreement with those computed by other approximate methods.