The problem of interaction of rod centralizers of casing with a well wall is considered. The paper aims at studying the ways of fastening of centralizer’s ends on the parameters of its rigidity and strength. Knowledge of these characteristics is necessary for the assessment of casing column drift and well completion quality. For simulation of the working links of the centralizers, the classical linear theory of smooth rods, rigid along the axis and elastic on bending is used. Stress-strain state of bow-type rod with six different variants of fastening under conditions of point contact is studied. The analytical relations between the contact force and the mutual approach of the column and the well wall, as well as the expressions for the admissible contact loads, are established. The way of fastening the rod significantly influences these characteristics; in particular, the fact of the presence or absence of freedom of mutual movement of its ends along the pipe is decisive. The engineering formulas, which serve as two-side estimations of the rigidity and strength of the real structures of centering devices, are obtained. A comparative analysis of mechanical properties of centralizers has been conducted.