The article presents a method to calculate complex eigenvalues of the problem modeling the rotation of ocean drill column for drilling of pore at the depth of thousands meters. The eigenvalue problem is formulated following \textit{T. Huang} and \textit{D. W. Dareing} [ASME J. of Eng. for Industry. May, 191-200 (1966)]. The corresponding ordinary differential equation of the fourth order takes into account the bending, torsional and longitudinal deformations, energy dissipation and added masses of water within the column and on the outside of the column. A solution of singularly perturbed problem is sought in the form of asymptotic expansion with a small parameter \(\epsilon\) for two parts of column: lower compressed-stretched part and upper stretched part. The developed method can be used for investigating the stability of working regimes of drill-column during the drilling deepwater pores.