Abstract: Toppling failure of rock slopes is associated with rock masses with a dominant discontinuity set with strike nearly parallel to the slope, dipping towards. The most frequent measures to control the slope are the installing of anchors or bolts, or lowering the slope angle by excavation, so it is important to determine the necessary anchor force to stabilize the slope. For this purpose, Goodman-Bray put forward with the theory of limit equilibrium of blocks, which considers the toppling failure of the blocks. It is based on the block theory, many assumptions are the same as the block theory. But the theory of limit equilibrium of blocks doesn t consider the influence of the block width on the anchor force. Lately, C.Sagaseta analyzed the influence of finite block thickness on anchor force of a particular case with Good-Bray method, the results show that the necessary force increases with decreasing block thickness, it reaches the asymptotic value when t →0, furthermore, the value is not far from the actual value in many cases. To gain the upper bound of the anchor force, the continuum method is adopted to analyze a basic case to gain the general solution. The block thickness is infinitesimal, hence the equilibrium equations in the Goodman and Bray method lead to ordinary differential equations that can be easily integrated in many cases. The solution can be considered as accurate for slopes higher than 20-30 times the block thickness. For thicker blocks, the anchor force may be reduced properly, which avoids project losing stability for smaller anchor force or economic loss for greater anchor force.