Purpose. Determination of deformation and force parameters that describe the strain-stress state of the casing string in non-vertical well-bore areas. Methodology. In a curvilinear well, the casing functions as a long permanent continuous rod. Its weight might cause some deformations that can be determined by a heterogeneous system of four differential equations. Taking into consideration the technological requirements for pipe installation on centralizers allows us to make the first integral of the system linear. Findings. It is proved that the elastic rod deformation under the impact of the longitudinal and transverse forces of the distributed weight can be calculated by a heterogeneous second order differential equation with variable coefficients. Its solution is the clue to the formulas of deflections, angular slopes, internal bending moments and transverse forces in the rod with the arbitrary arrangement of supports and boundary conditions in their intersections. Originality. The solution of the governing differential equation of angular deformations of a long bar is found in the form of a linear combination of Airy and Scorer's functions and in the form of three linearly independent polynomial series in the sum with a partial answer. Practical value. The obtained formulas of flexure and power parameters allow us to calculate stress and strain in the tubing during the process of casing the bore-hole of an arbitrary profile which increases the reliability and durability of the well.

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