This paper presents the experimental results the influence the effect of elastic deformation on the resistance R(ξ) and thermopower α(ξ), of bismuth-antimony Bi1-xSbx nanowires at 4.2 - 300 K. Glass-coated single-crystal Bi wires of different diameters (70 nm and 320 nm) were prepared by high-frequency liquid phase casting by the Ulitovsky method. According to X - Ray diffraction, all the wires had the same (1011) orientation along a wire axis. A rising tide of interest in thermoelectricity in recent years is due to development of new concepts, topological insulator and nanotechnologies, opening up new ways for enhancement of thermoelectric figure of merit both in the nanostructures. Thermoelectric figure of merit is defined by the expression: ZT=, where α is thermopower, σ is electric conductivity, χ = χe +χp , χр is lattice thermal conductivity, χе is electron thermal conductivity along the wire axis. One of possible methods of thermoelectric parameters control is elastic deformation whereby there is an essential change in the Fermi surface topology in Bi and its alloys. It was shown that elastic deformation in glass – coated single crystal Bi nanowires can reach 2 – 3 % of relative elongation, which brings about essential changes in the Fermi surface topology. We found that with decreasing diameter of the nanowires, the temperature range of exponential growth of the resistance shifts into a higher temperature region and the energy gap dE increase due quantum confinement as dE=1/d. We also observed that the small diameter wires at law temperatures show a sharp deviation from the behavior of the resistance R(T),characteristic of semiconductor. That can be interpreted in terms of the surface states in topological insulators Bi1-xSbx nanowires. It was shown that the elastic tension the Bi1-xSbx nanowires lead to an increase in absolute value of thermo-power and decrease of the resistance. That leads to growth the thermoelectric figure of merit Z and opens up a principally new route for drastic enhancement of the thermoelectric figure of merit Z.