In order to solve the shortcomings of the classical model of in-situ stress measurement based on the breakout shape of wellbore, an analytical model of the stress around the deep non-circular wellbore is established by using the complex variable method and conformal mapping. The coefficients of conformal mapping function are solved according to Melentiev method, and the correctness of coefficients is verified. Through the boundary conditions of non-circular wellbore, the coefficients of complex potential functions and wellbore stresses are solved, and the analytical results are verified by commercial finite element software. By selecting different drilling fluid pressure and far-field stress ratio for sensitivity analysis, the variation trend of hoop stress and the influence on wellbore stability are explored. The analytical model can provide a theoretical reference for the analysis and solution of the mechanical behavior around the wellbore in deep drilling under the conditions of high temperature, high pressure and high ground stress, and lay a theoretical foundation for explaining the development process of wellbore breakout and developing the modified model of deep in-situ stress measurement based on wellbore breakout shape.