The circular rock stratum are inevitably encountered in underground mining engineering, which causes waste of resources and dynamic instability. Based on the elastic theory of curved beam and finite-difference computation, a displacement function is presented in polar coordinates for solving two partial differential equations with the boundary conditions in mixed type in elastic, isotropic and homogeneous rock. A semi-analytical elastic stress solution for circular rock stratum is obtained according to the governing equation and stress components in terms of displacement function. The variations of stress distribution with different influencing factors are analyzed, which may lead to a better understanding of the stability of circular rock stratum after coal extractions. Finally, this semi-analytical elastic stress solution is applied to the fold structure in No.2502 mining area and points out the dangerous sites during coal extractions, which provides the basis of construction and safety in coal mine engineering.