Book excerpt: The Distinct Element Method (DEM) and Discontinuous Deformation Analysis (DDA) are the two most commonly used discrete element methods in rock mechanics. Discrete element approaches are computationally expensive as they involve the interaction of multiple discrete bodies with continuously changing contacts. Therefore, it is very important to ensure that the method selected for the analysis is computationally efficient. In this research, a general assessment of DDA and DEM is performed from a computational efficiency perspective, and relevant enhancements to DDA are developed. The computational speed of DDA is observed to be considerably slower than DEM. In order to identify reasons affecting the computational efficiency of DDA, fundamental aspects of DDA and DEM are compared which suggests that they mainly differ in the contact mechanics, and the time integration scheme used. An in-depth evaluation of these aspects revealed that the openclose iterative procedure used in DDA which exhibits highly nonlinear behavior is one of the main reasons causing DDA to slow down. In order to improve the computational efficiency of DDA, an alternative approach based on a more realistic rock joint behavior is developed in this research. In this approach, contacts are assumed to be deformable, i.e., interpenetrations of the blocks in contact are permitted. This eliminated the computationally expensive open-close iterative procedure adopted in DDA-Shi and enhanced its speed up to four times. In order to consider deformability of the blocks in DDA, several approaches are reported. The hybrid DDA-FEM approach is one of them, although this approach captures the block deformability quite effectively, it becomes computationally expensive for large-scale problems. An alternative simplified uncoupled DDA-FEM approach is developed in this research. The main idea of this approach is to model rigid body movement and the block internal deformation separately. Efficiency and simplicity of this a.