In view of the instability of the excavation face of the sandy cobble stratum, the research on the theoretical model at the present stage is relatively less, and the application of the supporting force of the shield machine in the construction mainly depends on the construction experience. In order to study the instability of excavation face in sandy cobble stratum, the calculation method of limit analysis model of excavation face of shield tunnel was established by using the upper bound theorem of limit analysis method and ellipsoid drawing theory. The two working conditions of the deformation of the square stratum before the excavation were studied, and the upper limit analytical solution of the ultimate supporting force was obtained. Five typical theoretical analysis methods were selected to verify the correctness of the calculation results. The results show that the ultimate supporting force of the excavation face obtained by the proposed logarithmic spiral ellipsoid mechanism is greatly affected by the friction angle in the stratum, the diameter of the tunnel and the weight of the stratum, while the influence of buried depth and cohesion is small, and the influence of surface overloading is the least. Among them, the ultimate supporting force of excavation face increases linearly with the increase of stratum weight and tunnel diameter, and decreases nonlinearly with the increase of friction angle. Compared with the rotational failure mechanism, 3D logarithmic spiral mechanism and the collapse area in front of the excavation face obtained by FLAC^3D numerical simulation, the collapse mechanism and numerical simulation in front of the excavation face can approach the failure shape of the stratum.