Initiation devices used in mining have strict requirements for safety and efficiency. However, the analysis of their operation is encumbered by their complex design which involves multiple explosive charges and inert materials. We use numerical simulations to study detonation in configurations involving complex geometry and multiple materials with the aim of revealing key features of their internal processes and improving their reliability and performance. The mathematical model is based on a two-phase reactive formulation and is extended with porosity and shock desensitization models. It is coupled with appropriate inert material models for fluids and solids to accurately capture their interaction with the detonation wave. We initially consider detonation propagation in annular charges. The model and implementation are validated against experimental data for steady state propagation. Then, the numerical solution is used to obtain a detailed description of the speed of the detonation wave along the annular arc and a new description of the transition phase is proposed. Further, a parametric study is performed in which the dependence of the transition phase and steady state on the dimensions of the annulus is analysed. The rest of the thesis examines detonation in explosive devices used in the initiation of tertiary explosives in mining. First, we consider the response of a detonator in isolation, guided by an underwater explosion test. Following validation, the strength of the blast wave is examined at several distances from the detonator. Results show that the blast wave in the near field is asymmetric and stronger along the axis of the detonator. Further, the near field blast wave varies considerably between detonators of different shell material and thickness while the pulse in the far field is similar. This indicates that the fine differences between detonators cannot be captured by tests that consider the blast wave at a single point in the far field. Lastly, we study the complete configuration used to initiate explosives in mining blastholes which involves a detonator and a booster. The reactive model is extended to account for shock desensitization. The model is validated and a series of simulations of the detonator and booster configuration, with and without desensitization, are performed. These show that the influence of desensitization is significant and can lead to the formation of dead zones in the explosive which have a critical impact on booster performance. Depending on the material of the detonator shell, the initiation of the booster can result in only a small non-reacted region or in an extensive desensitized zone which prevents the detonation of a large portion of the explosive.