ABSTRACT: A horizontal circular opening is excavated in a transversely isotropic rock mass. It possesses a plane of isotropy. The plane is inclined to the horizontal axis of the cross-section of the opening. The stresses at a point of the hole are determined by the complex potential theory. The behavior of the rock mass is described by a fourth-order partial differential equation. Its characteristic equation is of the fourth degree. An iterative method was used to determine its roots. These roots are complex numbers and are involved in the analytical expressions for the stresses along the hole contour. The coefficients in the characteristic equation and its complex roots are determined for a real rock mass. The values of the stresses at points on the contour of the hole were calculated.