By adopting the irrotational and steady motion of the ideal compressible fluid and the supercavity with the Riabushinsky scheme of closure,an integro-differential equation was derived for the supercavitating flow around a slender cone-shaped projectile traveling in water at subsonic speed by using the slender-body theory and the matched-asymptotic-expansions method. The first-and second-order approximation solutions for the supercavity shapes considering the compressibility effect were obtained,and the calculation precision was improved. The influences of the flow compressibility on the supercavity profiles were analyzed under the high-speed impact of the gun-launched projectile. With the increase of Mach number,the supercavity shape expands markedly. The calculated characteristic parameters for the supercavity profiles are in agreement with the theoretical and experimental results.