The stability of the tunnel face is an essential consideration in tunnel design. When it is not possible to maintain tunnel face stability under natural conditions, it is essential to intervene with extremely expensive reinforcing operations. Numerical models and simplified analytical models can be used to accomplish a detailed analysis of the stability conditions of the tunnel face. There are simplified analytical models for shallow tunnels, but there are few for deep tunnels. This work proposes a closed-form solution for the analysis of face extrusion deformation with reinforcement during full-face tunnel excavation based on the theory of spherical symmetry in homogeneous initial stress. It is worth noting that the proposed approach is both simple and applicable. It also provides a new mathematical concept for the design of fiberglass dowels and is useful for real engineering applications. The proposed model's accuracy and applicability are validated by comparing it with numerical simulation. The results show that with the increase of various parameters, the extrusion deformation decreases gradually, which reveals that improving the strength of the face plays a significant role in ensuring its stability. The comparison shows that the proposed model in this paper has higher accuracy for the squeezing tunnel. In addition, when the reinforcing radius RL increases, the extrusion deformation value of the tunnel face falls steadily. However, when RL increases, the relative control impact decreases. When the reinforcement radius RL increases, the extrusion deformation value and the influence of relative control of the tunnel face decreases. Thus, under the same reinforcement strength, there is a reasonable reinforcement radius range, which should be determined in combination with engineering safety and economy.