The statistical theory of the dipole flexoelectric (FE) polarization in liquid crystals is used to calculate the temperature dependence of order parameters, the elastic constants and the FE coefficients. Two systems with polar wedge-shaped and banana-shaped molecules are investigated. In both cases the FE coefficients are proportional to the dipole moment component parallel to the molecule symmetry axis. The origin of the FE effect and microscopic pictures of the distorted phases are discussed.