Layered rock masses exhibit pronounced mechanical anisotropy, and bedding discontinuities can substantially alter excavation-induced stress redistribution and concentration around a tunnel, thereby increasing the likelihood of instability. In this study, a three-dimensional discrete-element numerical simulation platform was employed to investigate a tunnel excavated in layered rock with bedding dip angles of 0°, 30°, 60°, and 90°. The distributions and evolution of the vertical and horizontal stresses were examined for the four configurations. The results indicate that tunnel excavation causes marked redistribution of both the vertical and horizontal stress components. The disturbance is concentrated in the near-field region and gradually diminishes with increasing distance from the opening. Vertical compressive stress is primarily concentrated near the crown and invert, whereas horizontal compressive stress is mainly localized along the sidewalls and extends toward the arch shoulders and feet. Approximately symmetric stress patterns are obtained for bedding dip angles of 0° and 90°. By contrast, at 30° and 60°, the stress-concentration zones migrate along the bedding direction, producing a distinct asymmetry between the two sides of the tunnel. These findings provide a theoretical basis for stability assessment and support optimization in tunnels constructed in layered rock masses.