The paper proposes an improved design of a shock absorber used in drilling deep oil and gas and geothermal wells with polycrystalline diamond compact (PDC) bits. The proposed innovations successfully combat the dangerous phenomenon of self-excited vibrations, which can lead to malfunctions such as stick-slip and whirling of the drilling tool. Most conventional drill shock absorbers are designed to only absorb longitudinal vibrations, which was sufficient when using roller cutter bits for the drilling process. However, the design features of PDC bits and the phenomenon of interaction of their cutters with interlayered rocks during deep drilling impose new requirements on the properties of the drill shock absorber. To protect the downhole tool from abnormal torque values and torque oscillations, it is proposed to equip the shock absorber with a special torque transmission unit in the form of a fourteen-thread self-releasing screw pair. This unit is capable of transforming increases in external torque into increases in the force that loads the elastic element of the shock absorber. The numerical and analytical models of the mechanism of transferring external axial load and torque to the elastic element of the drill shock absorber are constructed. The distribution of contact pressures on the interacting surfaces of the screw pair and the distribution of equivalent stresses in the screw pair parts are analysed. The strength of the proposed drill shock absorber assembly was evaluated using the Huber-von Mises energy criterion. The dependence of the load transmitted to the elastic element of the shock absorber on changes in the external torque and external axial force is investigated. In general, it is determined that the external load is distributed evenly between all turns of the screw pair, and the limit state of the parts of the proposed assembly is not reached even under high-torque operating load. The obtained analytical dependencies will allow to effectively determine the required strength and stiffness of the elastic element of the drill shock absorber at the design stage. The obtained analytical results were verified using a finite element model.