The operation of oil and gas wells with sucker rod deep well pumping units takes place in aggressive conditions of the oil and gas production field. This leads to accidents arising with deep well pump rods of these units. The report talks about the possibility of eliminating accidents arising with glass fibre rods, which differ from metal, steel rods by their physical and mechanical properties. These rods are the most important part of a deep-water pumping unit. It is noted that in order to eliminate accidents with deep-well pumping units it is necessary to develop a catching tool rod-header. The diameters of these rods used in production are specified. It is noted in the report that fibreglass rods are made in order to save metal, as well as these rods are anticorrosive in comparison with metal rods. The disadvantage of fibreglass rods is their relatively low strength (σ) compared to metal, steel rods and their smoother surface, which is less able to be effectively gripped by the rod head. The report explains the process of eliminating a fibreglass rod accident with this catching tool. Continuing the lowering of the rod-header there is a gripping inside the tool body by the surface of the coupling or body of the fibreglass rod by gripping elements, spiral parts and collet. The efficiency of the process of gripping of the glass fibre rod depends on what, as a result of this, it is possible to eliminate the accident in a well with oil and gas producing deep well pumps with the help of the rod head developed for glass fibre rods.