Fluid flowing through reservoir pores not only generates poroelastic stress but also exerts seepage force on rock skeleton. However, the mechanism of seepage force is not clear. Traditional methods of analyzing wellbore stability and hydraulic fracture initiation are mainly focused on the poroelastic stress without the effects of seepage force. Based on the linear elasticity and consolidation theory, this paper analyzed the mechanism of seepage force and poroelastic stress, and presented an analytical solution for seepage force-induced stress around a vertical wellbore. It also introduced how to calculate poroelastic stress by exerting hypothetical body force and surface force. Through comparison and superposition of stress fields, this paper studied the change characteristics of the poroelastic and seepage force-induced stress under different borehole pressures and the effects of seepage force on the wellbore tensile failure. Numerical simulation results show that when fluid flows through the rock, using traditional models without considering, the effect of seepage force to calculate the borehole pressure-induced stress will result in lower calculation results. Compared with the traditional model, seepage force-induced circumferential tensile stress is larger, and the seepage force significantly reduces the formation breakdown pressure. Rocks near the borehole wall with lower permeability and larger Poisson’s ratio have a greater action of seepage force. When fluid flows through the reservoir, the effects of seepage forces cannot be ignored in the analysis of hydraulic fracturing and wellbore stability.