This paper deals with simulating the energy-saving regimes of drilling deep curvilinear bore-holes with prescribed geometrical imperfections of their axial lines. On the basis of the theory of curvilinear flexible elastic rods, the 3D “stiff-string” drag and torque model of the drill string (DS) bending is elaborated. With its use, it is shown that the contact and friction forces generated by interaction of the DS with the bore-hole surface can be regulated through the combination of its axial and rotary movements. The advanced is applicable for monitoring the ascending–descending operations, drilling, and well completion.

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