The flashover in vacuum is a rapid interfacial discharge across the insulator surface when subjected to high applied voltage. Here a theoretical model covering above-surface processes is introduced. The model calculates the flashover threshold in vacuum, with revised secondary electron emission avalanche theory and improved desorbed neutral transport model. The model serves as the first part of an integrated flashover model, aiming for consistent treatment of both above-surface and subsurface processes during the entire flashover development. The flashover threshold is obtained by combining the desorbed neutral pressure at given applied voltage and the gas breakdown criterion dictated by the Paschenâ\euro™s law. An analytical formula for threshold estimation containing physical parameters, and a simplified formula consisting of empirical coefficients are introduced, catering for both conceptual understanding and practical application. The derived formulae are validated by experimental data for a variety of insulator materials. The theory generalization for nonuniform electric field distribution is further discussed.