Formation of bipolaron states is investigated at interaction of two same carriers of the charge which are being non-polar quantum wire placed in polar environment. Alongside with effects of dimensional quantization of an electronic spectrum, quantization phonon spectrum is considered. "Inoculating" quasi-particle in a considered problem are electronic polarons at which allocation interaction with plasma vibrations of valent electrons (fast polarization) is accepted in attention. It is shown, that in case when the radius of a wire surpasses much more radius of electronic polaron, interaction of carriers considering only fast polarization is well described by the potential of interaction received within the limits of classical electrodynamics. The contribution into screening interactions of slow (ionic) polarization of the polar environment surrounding not polar wire, is defined by effective potential electron-phonon interactions of structure which is received by averaging on oscillator variables of electron-phonon interactions exact Hamiltonian. Using results of numerical calculations, structures of potential energy of interaction of the same carriers for various sets of parameters (high-frequency permittivity of a wire and its radius and high-frequency and low-frequency permittivities of environment) are constructed. It is shown, that for favourable combinations of parameters (small radius of a wire, a greater difference between high- and low-frequency transmittivities of environment) in the potential of interaction of the same charges it is probable formation of area of an effective attraction that leads to their binding in bipolaron pair with binding energy, on one-two orders of the corresponding pair exceeding energy in a volumetric crystal with the same values of material parameters. It can have defining value in an explanation, for example, of such effects, as high-temperature superconductivity, in structures with quantum wires.