The proxel-based method is an intuitive approach to analysing discrete stochastic models, such as are described by stochastic Petri nets or queuing systems for example. The approach analyses models in a deterministic manner, avoiding the typical problems of discrete-event simulation (e.g. finding good-quality pseudo-random-number generator) and partial differential equations (difficult to set up and solve). The underlying stochastic process is a discrete-time Markov chain which is constructed on-the-fly by inspecting all possible behaviours of the model. The proxel-based simulation is shown to be very useful in analysing some classes of reliability models and fault-trees. In particular it is more efficient than the discrete-event approach applied to the same models, because the proxel-based method is less sensitive to the stiffness of the models. The goal of the thesis is to formally define this new method, study its behaviour under different circumstances, as well as show that it can be more suitable than some existing methods for certain classes of problems. Further, the thesis examines some of the application areas of the proxel-based method.