By means of a generalized three-level solvable model, the self-consistent procedure for solving the Hartree-Fock (HF) equation is studied in detail. It is pointed that some attention should be paid to the multiplicity of the solution. Different criteria for choosing a proper solution are considered and discussed. The reason for the sudden jump of the HF solution in some force-parameter (FP) regions, the stability of the HF solution and the FP dependence of the solution are also investigated.