The problem of electron binding in solutions is treated on the basis of a continuum model. The polarizable medium is represented by a continuum, which can be characterized by macroscopic properties, e.g. the static and the optical dielectric constants. The motion of an additive electron is determined by its interaction with the polarization produced by the electron itself. An attempt is made to treat the whole system (dielectric medium and additive electron) by employing two different approximations. After the separation of the electronic and nuclear motion, an adiabatic separation of the motion of the medium electrons and the additive electron is carried out. An alternative approach involves the application of the Hartree-Fock self-consistent-field treatment. A comparison of these treatments is presented. It appears that the independent particle approximation is adequate for the treatment of electron binding in solutions. The adequacy and scope of the continuum approximation are discussed.