The main goal of this talk is to construct a detached shock solution of the steady Euler system for inviscid compressible irrotational flow. In particular, we seek a shock solution with the far-field state being the strong shock solution obtained from the shock polar analysis. Furthermore, we prove that the detached shock forms a convex curve around the blunt body if the Mach number of the incoming supersonic flow is sufficiently large, and if the boundary of the blunt body is convex. This work is collaborated with Myoungjean Bae.