Abstract：The stress distribution and plastic zone range of roadway surrounding rock are important reference indexes for the design of roadway support parameters. Because the section shape of rectangular roadway is easy to cause stress concentration, taking the return air roadway of 3202 working face under the influence of Wangcaihuopan mine fire area as the engineering background, based on the theory of complex variable function, the mechanical model of surrounding rock stress of rectangular roadway is established, and the complex variable function solution of surrounding rock stress and its plastic zone range are obtained. The influence of roadway aspect ratio and lateral pressure coefficient on stress distribution and the factors of plastic zone development of surrounding rock are analyzed. The comprehensive support scheme of optimizing bolt ( cable ) support, using I-steel shed to suppress roadway surface deformation and grouting to improve the mechanical properties of surrounding rock is put forward. The research results indicate that the stress distribution of the surrounding rock in rectangular roadways exhibits significant non-uniform variations, particularly with noticeable stress concentration at the shoulder corners of the roadway. The development of the plastic zone shows a typical ' X '-shaped distribution characteristic, and this failure mode is significantly coupled with the stress redistribution process in the corner regions of the roadway. The optimized support scheme significantly improves the distribution range and stability of the stress concentration area of the surrounding rock, reduces the deformation of the roadway roof and two sides, effectively controls the deformation of the surrounding rock of the roadway, and forms a good coupling effect between the support body and the surrounding rock. Through field engineering practice, it is verified that after adopting the optimized support scheme, the roof subsidence is 37 mm, and the two-side shrinkage is 19 mm, and the control effect is remarkable. Keywords: stress distribution of surrounding rock; complex variable function solution; support optimization; numerical simulation; field application