In this work, we study the conductivity of nanowires (NW) based on anisotropic semicoductor or semimetal in transverse magnetic field H||Oy at low temperatures. The confinement of NW is parabolic (the NW axis is Ox)formulaare the constants of NW; mi is the component of tensor of effective masses for electrons (with (h) for holes). The conductivity of NW contains the contributions of electrons and holes and is determined with the use of the Kubo formula [1, 2] in the case, when the basic mechanisms of carrier scattering are assumed to be elastic acoustic-phonon scattering and scattering on a roughness surface of NW. Taking into account [2, 3], for the resistance of semiconducting NW (the conductivity is determined mainly by the contribution of electrons) we can write:formula is the Bohr magneton; gc (gv) is the g-factor for electrons (holes); m0 is the mass of electron; c is the light velocity; T is the temperature; k0 is the Boltzmann constant; Δ0 is the band gap or overlaping of bands (Δ0 < 0) of crystall. The magnetoresistance of semiconducting NW can be positive or negative and depends exponentially on magnetic field, temperature and wire diameter. For a semimetallic NW (with the lowest occupied subbands) the resistance isformulaξ is the chemical potential. For some directions of magnetic field the magnetoresistance can be negative. Those results are close to experiments for NW based on Bi with a diameter of 50–100 nm [4].