Abstract：Three key issues are included in three-dimensional discontinuous deformation analysis(3D-DDA)；they are identification of block，creation and solution to motion equations of individual unit，the detection and updating of varying contacts between the units as the consequences of their motions and deformations. For these questions，three-dimensional block geometric identification algorithm was formed through the boundary operator according the concept of simplex and simplicial complex in algebraic topology. To ensure the accuracy of block identification，Euler-Poincaré formula was adopted. And simplex integration is used to obtain the analytical solution of block physical characteristics quantity. Then based on first order displacement mode，global equilibrium equations of three-dimensional discontinuous deformation analysis system was proposed in accordance with the principle of minimum potential energy. According to failure characteristics of rock mass engineering，a face-face contact model was created；on this basis，factor of safety of rock slope was calculated using strength reduction method. It is known from the example of simple wedge failure that the problem caused by assumptions of limit equilibrium method can be solved by 3D-DDA，which could calculate the correct factor of safety for wedge stability. The engineering slope example shows that，through the research on rock slope stability by 3D-DDA，rock slope failure mechanism could be understood deeply；and the location，volume，sliding direction and the corresponding support methods of critical sliding block could be easily determined. In addition，considering that DDA could accurately solve the tangential sliding force，the reasonable factor of safety could be obtained by combining strength reduction method.