Under the assumption of small relative thickness of a body and small ratio of gas densities at the front of an incident wave falling upon a body, irregular interaction of a strong shockwave with a thin pointed body of revolution is investigated. The reflected wave is assumed to be weak and contiguous to the body point. The problem is reduced to an integral differential equations system for defining the front of a Mach wave in quadratures. In the self-modeling case of a strong shockwave reflected from a thin cone, the problem is reduced to integrating an ordinary differential equation to determine the front of a diffracted shockwave.