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The article presents the main factors affecting the buckling when drilling vertical wells. The authors study analytically the effect of the weight on the bit and the force of the interaction of a drill string with a borehole wall using a uniform-sized arrangement of the bottom-hole assembly and the borehole wall which is located in a deviated wellbore when drilling in isotropic rocks in case the drilling direction coincides with the direction of the force acting on the bit. Differential equations of the elastic axis of the drill string are worked out. The solutions of these equations have given nondimensional dependences between the technological parameters. The authors have obtained the graphical dependences of the distance from the bit to the “drill string - borehole wall” contact point and the normal reaction of the bottom to the bit and the “drill string - borehole wall” clearance. The dependence for identifying the drilling anisotropy index in oblique beds is obtained. An interrelation between the anisotropy drilling index, the zenith angle, the bedding angle, the bottom-hole assembly, the borehole dimensions and the axial weight on the bit has been established. The authors have studied analytically the effect of the weight on the bit and the force of the “drill string - borehole wall” interaction, when installing the centralizer to the bottom-hole assembly. The differential equations of the elastic axis of the drill string with the centralizer in the bottom-hole assembly are obtained. It is established that with the increase in the axial weight on the bit and the “drill collars - borehole wall” clearance, the distance from the bit to the contact point of the borehole wall decreases; whereas with the increase of the deviation angle and the clearance, the pressure force of the column on the walls increases. It has also been established that the anisotropy drilling index reduces the distance from the bit to the point contact both in a slick BHA and in the bottom hole assembly with the centralizer. The presence of a centralizer in the bottom hole assembly increases the distance from the bit to the contact point between the string and the borehole wall, makes it possible to increase the weight on the bit without the risk of increasing a deviation angle.