The purpose of this paper is the exploration of the electric field structure near cylinrical bodies. The solution of the problem is reduced to solving the equation for the potencial of a self-consistent electric field written in dimensionless form. The behavior of the potential is found by the combined method (at the initial stage, analytically, and then numerically). In contrast to the works devoted to this subject, the dependence of the potential on the coordinates is determined at various values of the electric field strength on the surface of the bodies, which is considered as a parameter. Such an approach made it possible to distinguish different regimes of electron flows motion: motion in an accelerating field, motion in a field with a minimum of the potential, and returned flow. Determining the position of the boundary between the second and third regimes made it possible to find the thickness of the shielding layer near isolated cylindrical bodies under conditions of deep vacuum. Knowledge of the potential and magnitude of the screening layer have a practical value: for radio communications, for the smooth operation of electronic equipment on artificial celestial bodies, for studying the mechanisms of lunar soil erosion caused by electric fields, for studying the behavior of potential in complex dusty crystalline structures, as well as for constructing cylindrical diodes working in a given mode.