The distinct element method (DEM) is a useful tool in rock engineering to model jointed rock masses. To simulate a jointed rock mass realistically, the main challenge is to be able to capture its complex geometry which consists of blocks with various shapes and sizes, and to model the interactions between these blocks. The main contribution of this thesis is the development of novel algorithms in the DEM to model jointed rock masses, namely rock slicing procedures for block generation, and algorithms for contact detection between polygonal blocks in 2-D or polyhedral blocks in 3-D. These algorithms make use of convex optimisation techniques, for which there exist efficient solution procedures. They do not rely on conventional vertex-edge-face hierarchical data structures and tedious housekeeping algorithms. The algorithms have been verified against analytical and numerical solutions, as well as validated against experimental results published in the literature. Among those, the results of DEM simulations were compared against the experimental model tests and numerical simulations of jointed beams carried out by Talesnick et al. (2007) and Tsesarsky & Talesnick (2007) respectively. Emphasis was placed on modelling the stiffness of the block interfaces accurately, and this was accomplished by reinterpreting the laboratory data published by the investigators. The capabilities of the numerical tools are also examined and demonstrated in areas for which the DEM has found practical application. A substantial fraction of this thesis is devoted to illustrating how these tools can assist the engineer in designing support systems; for example, designing the length and spacing of rock bolts and the lining thickness for a tunnel. Algorithms to model rock bolt and lining support were implemented for this purpose. Interesting comparisons with elastic solutions for supported openings were obtained. Further, it is shown that the relative benefit of introducing more rock bolts or thicker lining can be evaluated using the numerical tools with the aid of an interaction diagram. In the final part of this thesis, the case history of the 1963 Vaiont rock slide in Italy is studied. The 2-D analyses led to useful insights concerning the influence of the reservoir water level, the rock mass strength and deformability, and the slide surface shear stiffness. 3-D analyses were undertaken to investigate the influence of the eastern boundary of the slope, and interesting insights were obtained concerning the slope kinematics. Overall, the case study shows that the tools are capable of modelling problems with specific physical and geometrical detail in both 2-D and 3-D.