The discovery of genetic regulatory networks was an important advancement in science. Not only do they help understand how organisms behave but the development of synthetic genetic networks has aided in other fields of science and industry. Many genetic networks have been modelled deterministically by using differential equations to provide an insight into the network's behaviour. However, within a biological environment, a certain degree of intrinsic noise should be expected and the robustness of these networks should be tested. Creating and analysing a genetic network in a biological environment can be a time consuming task so applying stochastic methods, such as the Gillespie Algorithm, to a computer model will provide an important, initial insight into the behaviour of the system. One interesting genetic network is the coupled repressilator due to its relatively simplistic design and the broad, multistable dynamics it offers. The inhomogeneous solutions that it can yield are particularly interesting as they may help explain certain biological phenomena, and may be used as a tool to assist with further research into genetic networks. In this thesis, the Gillespie Algorithm will be applied to the coupled repressilator so that its robustness can be tested. Biologically feasible modifications will be made to the system to produce much more stable and predictable dynamics so that the broad range of solutions can exist within a noisy environment. The methods developed will take into account previously made assumptions and potential errors in biological data so that they can be applied to other genetic system. One further objective in this thesis is to explore computational limitations that may occur when modelling large, stochastic networks. Issues such as rounding errors and dealing with very small and very large numbers were encountered and methods to circumvent these without sacrificing computational run-time will be developed and applied.