A large number of biological systems can only be understood through computer simulations. Prototypical examples in popular science are insect swarms and ant colonies, but the same holds true for many other biological phenomena. For example, the progression of a disease in a host tissue (cell invasion), the propagation of viruses, or the formation of bacteria films can often only be predicted using simulations. From the perspective of computational modelling, all these systems are similar: a large number of individual elements move, proliferate or change state according to simple rules that are only based on local information. While simulations of such systems are often conceptually simple, they put extreme strain on computational resources. It is not unusual for a single simulation run to take many hours or even days and often thousands of runs are required. This currently renders many interesting simulation experiments infeasible in practice. GPU computing promises a solution to this problem. Graphics procesesing units (GPUs) have special purpose architectures that perform computer graphics operations in parallel at extremely high speed. Somewhat surprisingly, the parallel processing capabilities of GPUs can also be used to speed up many types of scientific computations by several orders of mangnitude (at extremely low cost!). The project will explore such parallelizations for common simulation algorithms, such as the Gillespie method, and use these algorithms to build simulations for selected problems in swarm behaviour and tissue modelling.