In order to ensure the electron emission stability from cathode filament of vacuum fluorescent display (VFD), the simplified model of filament deformation was established, the analytical formulas of deflection and maximum stress under an impact load were deduced, and the reliability of the analytical solution was verified by comparing with the finite element results. The criterion of structural parameter design was proposed. The results show that the analytical formula accurately describes the mechanical properties of VFD cathode filament under different impact loads. The maximum deflection and the maximum stress occur at the position where the impact load and the midpoint of VFD filament coincide, both of them increase with the filament lengthening or thinning, and the diameter has more obvious effect on the increase. The design criterion related to length and diameter of VFD filament is accurate, efficient, simple and feasible. The research results can offer qualitative support to the reliability design of VFD filament, and provide quantitative basis for the optimization design of structural parameters to improve its performance.