The problem of computer simulation of mechanical behavior of drill strings in hyper deep vertical, inclined and horizontal bore-holes is stated with the aim of forecasting the possible initiation of emergency situations during carrying out drilling operations. The question of stability and post-critical non-linear deforming and dynamics of the drill strings are considered. It is shown that all of them are singularly perturbed from the mathematical point of view and because of this, they are poorly amenable to theoretical (computational) analysis. The algorithms allowing surmounting these difficulties are proposed.The software for study of these phenomena is elaborated.In the stages of design of an elongated curvilinear bore-hole with complicated 3D geometry and technological regimes of their drivage, the elaborated software permits one to construct its trajectory securing the smallest values of resistance forces and to choose the least energy-consuming and safe regimes of drilling. It ensures also the possibility to determine the requirements for the necessary accuracy of the bore-hole drivage and for the acceptable geometrical distortions and imperfections.In the stage of the bore-hole drivage, the created software permits to calculate forces and moments of resistance forces with allowance made for the real geometry of the bore-hole and admitted distortion of its axial line. It is possible to prognosticate possible emergency situations and design the measures for their exclusion. At the stage of the emergency situation liquidation, this software allows to simulate the mechanical behavior of the system and its responses to the methods used for elimination of the failure consequences.

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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 o f 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.