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Fluid seepage into rock pores not only generates poroelastic stress but also exerts seepage force on the rock skeleton. However, since the mechanism of the effect of seepage force on the stress field around the wellbore is not clear, conventional methods calculate the stress field only taking into account the poroelastic stress without the coupled effects of seepage force and rock deformation. Based on the theory of porous medium, this paper presents an analytical solution of the circumferential stress field formed by the seepage force around the wellbore and introduces the solution into traditional calculation models to overcome these issues. The numerical study by MATLAB® was used to simulate the stress field around the wellbore. Numerical simulation results show that the seepage force generates a circumferential tensile action and reduces in-situ circumferential compressive stress around the wellbore. Under the effect of seepage force, the effective circumferential stress around the wellbore becomes smaller. When considering seepage force, effective circumferential stress along the θ = 0 direction at the wellbore wall is reduced by about 32% compared with traditional numerical results. In addition, the circumferential stress field formed by the seepage force increases the possibility of rock failure at the well wall. The analytical results indicate that the seepage force should be considered in the stress field calculation around the wellbore, especially in reservoirs with low permeability.