Analysis of breakdown mechanism in gas-insulated trigatron switches is important for the engineering design and function prediction. Based on the gas discharge theory, a physical model was proposed to estimate the breakdown time for gas-insulated trigatron switches. And the model can explain the breakdown in the trigatron switches with two modes of the breakdown mechanism, i.e., fast breakdown mode (FBM) and slow-breakdown mode (SBM). Based on Raether breakdown criterion, this paper discussed the factors affecting on the E-field enhancement. The E-field is composed of the static E-field and the dynamic E-field, which leads to transformation of breakdown mechanism. Some coefficients could be determined by experiment and simulation, which are helpful to get the quantitative solution of breakdown time.