The complex and non-linear nature of blast fracturing have restricted common blast design mostly to empirical approaches. The code developed for this investigation avoids both empiricism and large memory requirement in order to simulate the pattern of interacting radial fractures from an array of shotholes, at various burdens and spacings, and in simultaneous and delayed modes. The resultant pattern is analyzed and a fragment size distribution calculated. The rules governing the distribution of radial cracks and the way in which they interact are based on model scale experiments conducted by various investigators. Calculated fragment size- distribution agree with data from the field. Powder factor dependence of fragmentation results is also well described by the model. The effect of discontinuities on rock fragmentation by blasting is also incorporated into the model. Discontinuities which are open and filled with air or soil-like material affect destructively the transmission of strain waves and propagation of cracks in the rock mass. These discontinuities can be incorporated into the simulation by inserting cracks to represent them. The cracks representing discontinuities will then terminate the cracks produced by blasting where they intersect. On the other hand, tight joints without filling material or with filling material but with a high bond strength and acoustic impedance close to that of the medium do not affect in a negative way the transmission of shock waves in the rock mass. A mathematical model was developed to treat these discontinuities which was based on principles from Linear Elastic Fracture Mechanics theory and Kuznetsov's equation which relates the mean fragment size obtained to the blast energy, hole size and rock characteristics. / Master of Science