Abstract: Cavity expansion theory is widely used in geotechnical engineering problems as a mature theory tool. However, it is not applicable to the non-circular cavity expansion problem. The initial non-circular cavity on the physical plane is mapped to a unit circle on a phase plane by a conformal mapping method, and the displacement caused by the cavity expansion on the physical plane is transformed to the phase plane. The elastic solution of non-circular cavity expansion is presented by a plane complex variable elasticity method. This solution is compared with the circular cavity expansion, and the reliability of this study is verified. Then, the mechanics characteristics of the square cavity expansion are analyzed. The results show that this study is consistent to the present cavity expansion method when this study is degenerated to a circular cavity. The stress concentration appears at the corner of the square cavity when the square cavity is in the process of expansion, especially the stress increase rapidly at the polar angle range from 30^o to 45^o. The stress state where the distance away from the cavity center is more than 4 times a₀/2 (a₀ is the side length of the initial square) is close to the cavity expansion theory. The non-ax symmetric of the cavity only has an impact within a certain range from the cavity center. The impact can be ignored when the distance from the cavity center is more than a certain range.