The paper is dedicated to applied problems of dynamic stability of deformable systems. Dynamics of boring columns for shallow drilling (up to 500 m) applied in oil-gas extractive industry is considered. The purpose is investigation of influence of the drill rod's material properties of amplitude-frequency characteristic and stability of movement. Deformation of the drill rod is assumed finite. A model of a compressed-torsioned drill rod is considered within the nonlinear theory of finite deformations of V.V. Novozhilov. Dynamic of elastic movement for steel and dural drill rods applied in the extractive industry, resonant vibration modes and instability zone are investigated. The resonant vibrations of drill rods on the basic and higher (third) frequencies and their stability are calculated.