Abstract: Based on the space-charge wave small signal theory, an electron conductance model of each gap in the multi-gap coupled cavity, a model for mode stability analysis, was presented. The formulas of each gaps electron conductance in a three-gap coupled cavity were derived as an example. Through the theoretical and simulative method, the beam-loading of different cavity electric field modes was studied, and the beam-wave interaction and mode stability in the coupled cavity were analyzed. The calculation and analysis show that the electron conductances in different cavity gaps and gap field modes are clearly distinct. Compared with the electron conductances in the first and second gaps, the electron conductance in the third gap greatly depends on the beam voltage and gap distance, and therefore it has a principal effect on the beam-wave interaction in the cavity gap and the mode stability. In addition, the model can be used in the beam-wave interaction simulation of extended interaction klystron.