By extending the 2D explicit limit equilibrium solution based on normal stresses over the slip surface of the 3D slope

a simple and convenient method of 3D slope stability analysis is presented; it is applicable to general-shaped 3D slip surfaces. Firstly

the normal stress distribution over the 3D slip surface is initially assumed

it is then modified to satisfy all the three force equilibrium conditions. A quadratic equation is derived in terms of safety factor

it finally yields the explicit solution to the 3D safety factor. The proposed method has overcome some insurmountable difficulties encountered in the current methods of columns; and free of consideration of inter-column forces

satisfying the major equilibrium conditions and features; simple and practical computation process. Example studies show that the proposed explicit solution gives the 3D safety factor of a wedge identical to the analytical solution

agrees well with the rigorous limit equilibrium solutions of symmetrical slope. The method has been applied to the preliminary 3D stability analysis of a dam abutment; and the computation results offer a guidance for design of stabilization.