Abstract: Engineering rocks in hydraulic and hydropower projects are always in a tri-axial state of unequal principal stresses due to the effect of geo-stress, such as those in dam foundations, slopes or underground water diversion tunnels. Seepage characteristics of the jointed rock masses under such a state are very important to the safety evaluation and stability analysis of these structures. Research on the corresponding cases of rock mass with a single joint is essential and most basic. This paper summarizes the basic studies on the characteristics of seepage in a single rock joint under tri-axial stress state. We systematically review and analyze previous achievements in this type of seepage calculation and discuss the advantages and disadvantages of each seepage-stress coupling formula. Results show that a great disparity exists in the previous formulae, indicating that up to the present, no mature theoretical system has yet been developed for these flows. A more reasonable seepage-stress coupling formula is suggested for calculating a single rock joint in the condition of tri-axial stress state on the basis of existing formulae. The present study would help analysis on the seepage-stress coupling of jointed rock masses or other engineering rock masses.