The article provides brief information about a non-standard experimental setup developed in the laboratory of the St. Petersburg Mining University Well Drilling Department. The developed technique presented makes it possible to simulate well cleaning process of cuttings by incorporating the variation of the parameters (the zenith angle of the well, the volume flow and rheological properties of the cleaning agent, the rotation frequency, the number and length of the drill string half-waves) that cause buckling. For the first time, the positive side of the drill string (DS) buckling phenomenon is considered. A positive hydro-mechanical effect on mud plugs and improved well cleaning were revealed. The results of the experimental study confirm an intense difficulty in transporting cuttings to the surface at a critical zenith angle of the well of 55°. Regularities have been established making it possible to determine the effect of DS buckling on the cutting-carrying capacity when drilling deviated and extended reach wells. It is proposed to use hydromechanical impact on the accumulated cuttings by artificially controlling the resulting DS buckling in order to destroy the mud plug and increase the efficiency of well cleaning without the use of specialized devices. A conceptual solution aimed at implementing a method for hydromechanical destruction of mud plugs—the use of drill pipes equipped with a quasi-distributed differential measuring system of strain gauges based on a fiber-optic Bragg grating—is presented.