By aiming at the lack of bearing capacity calculation method in the current standard for trenchless reinforcement and repair of existing drainage main channel masonry arch culvert with arch vamp high-performance reinforced concrete, the design calculation formula of bearing capacity of the normal section of the arch roof and arch toe of arch culvert reinforced with arch vamp was proposed. Based on the analysis of the stress characteristics of masonry arch culvert reinforced by the arch belly, the calculation diagram of internal force was put forward. Based on basic assumptions, the design formula of bearing capacity of the normal section of the arch and toe was obtained. The results showed that the trenchless reinforcement and restoration with arch high-performance reinforced concrete could effectively prevent the emergence of plastic hinges. When the arch belly of a masonry arch culvert was strengthened by the method of the increasing section, the calculation schematic diagram could be calculated by the hingeless arch. The experimental data were used to verify the theoretical formula, which was in good agreement with the experimental data, which could be used for reference for the design of drainage arch culverts reinforced with brick masonry.