Developing "smart" materials with improved both structural and functional characteristics is one of the promising areas of materials science. Measuring the electrical resistance of CNTs-modified (various mass contents) polymers and in particular, elastomers during performing several tests (compression, stretching, and torsion) at a constant current is relevant in electrical engineering, mechanical engineering, aviation, and space industry. Changes in the elastomer shape under different types of testing lead to the destruction of macromolecules and the structuring of the material as a whole. Therefore, it is important to study the effect of CNTsbased modifying fillers on the elastomer. When compressing, stretching or twisting the nano-modified elastomer, along with the mutual movement of its macromolecular fragments and aggregates, the modifier particles also move, which generally determines the transport of electrons in the resulting structure and affects the physical and mechanical parameters of the composite material. To conduct studies, elastomers containing different amounts of a CNTs-based modifying filler were prepared. To investigate and elucidate relevant dependencies, a measuring system (MS) was constructed, which makes it possible to determine electrical resistance values of the composite material with different CNTs contents in the polymer matrix composition exposed to various mechanical loads. Basing the research results, it was established that the electrical resistance of the elastomer composites modified with 1.0–2.5 wt.% CNTs decreases when compressing from 0 to 100 N, whereas when the compression force ranges from 100 to 350 N, the electrical resistance remains unchanged. When the elastomer composites modified with 2–2.5 wt.% CNTs were stretched by 30–40 %, the electrical resistance was found to increase from 5·103 to 1.9·107 Ω.