The analysis of the general instability of stiffened cylindrical shells under hydrostatic pressure carried out earlier is continued in order to study the inversion of the eccentricity effect. 250 typical shells of varying geometries are considered. The results show that the inversion of the eccentricity effect is practically independent of the geometry of the rings but depends very strongly on the shell geometry parameter Z. A range of inversion is found. A detailed physical explanation of the causes of the eccentricity effect and its inversion is proposed.