A non-Euclidean continuum model for the descriptions of the elastic stress-field distributions and fractured zones in the surrounding rock masses around the deep circular tunnels subjected to nonhydrostatic pressure are established. In the non-Euclidean continuum model, the elastic stress-field distribution of the deep surrounding rock induced by compatible deformation of non-fractured zones and incompatible deformation of fractured zones is determined. The wavy behavior of the stress components based on the non-Euclidean model are obviously different from that of the stress components which have extrema on the working contour and tend monotonically to the value of the in-situ stress at infinity in rock masses within the framework of the classical model. Mohr-Coulomb criterion is applied to research the occurrence of disintegration zones. Disintegration zones appear when the stresses in deep rock masses reach a certain critical value. It is found from the numerical results that the magnitude and site of fractured zones depend on the value of in-situ stress and non-Euclideanness parameters.