Frequently, simplified partial differential equations include transcendental functions with analytical solutions based on a singularity. Such solutions are characteristic for numerical analyses with strong Solvers and several programs singularities in the processes of dressing rolling mills with lubrication. The devised dynamical model includes the variability of the gripping angle and of the rolls radius in a section of continuous rolling. Below the real lubricant layer, in the analysis two apparent lubricant layers are presumed. The solution of the differential equation of the lubricant layer with the singularity is obtained using standard mathematical solutions for apparent lubricant layers. On the ring diagram, the transfer over the singularity shows a stronger disorder, i.e., disharmony, than the transfer over the transcendental point.