Abstract: The stability analysis of roadway is essentially a three-dimensional space problem. Based on the generalized plane strain problem, the stress state of roadway under three-dimensional stress field is decomposed into plane strain state, out-of-plane shear state and uniaxial compression state. Taking the rectangular roadway as an example, the complex variable solution of the stress around the roadway under each stress state is solved by the complex variable function method, and the complete analytical expression of the stress component at any point around the roadway is established by the superposition principle. The differences between the complex variable analytical method and the equivalent circle method in the stress distribution and morphological characteristics around the roadway are systematically compared, and the implicit equation of the plastic zone boundary of the surrounding rock of the rectangular roadway is derived. The results show that the equivalent circle method ignores the local stress concentration effect of the rectangular roadway due to the simplification of the section, and the calculation results are significantly different from those of the complex variable analytical method. In particular, the stress concentration at the corner of the rectangle has a decisive influence on the shape of the plastic zone of the surrounding rock. The correctness of the proposed analytical solution is verified by numerical simulation. The theoretical method is applied to the field example analysis, and it is found that the complex analytical solution considering the axial stress component is in good agreement with the field failure mode. The new support scheme based on the distribution characteristics of plastic zone is proved to be effective in engineering practice. This study not only provides a theoretical basis for further understanding the plastic failure mechanism of roadway surrounding rock, but also provides technical guidance for numerical model verification, roadway support optimization design and roof fall disaster prevention and control.