Abstract: Rectangular roadway deformation is serious in deep mining, but the existing elastic-plastic theories are for the circular or elliptical roadways' stress analysis. Complex variable function method can deal with the mechanical problems of complex boundary shape. In order to solve the problem of rectangular roadway surrounding rock's stability, the complex variable function theory is used to analyze the stress of rectangular roadway. By means of complex variable function and viscoelastic theory, the rectangular roadway's stress concentration coefficient is derived, and the relations between stress concentration coefficient and time, different θ value are analyzed. The research results show that the stress concentration coefficient is decreased with time, the two sides of the roadway's stress concentration coefficient is bigger than coefficient in the roof and floor.