Abstract <p>In this paper, we study the ultimate deformed state of an isotropic rod under the influence of external pressure and varying linearly along its generatrix. It is assumed that the rod rotates around its axis. The general equations describing the limiting state of rods under the influence of external pressure in a cylindrical coordinate system are considered. Integrals of relations describing the ultimate deformed state of the rod are obtained. The characteristics of the studied ratios and the envelope of the family of characteristics are found. The deformed state of a cylindrical isotropic rod with a circular cross-section under external pressure is determined.</p>